Justice BREYER delivered the opinion of the Court.
The Federal Arbitration Act states that a "written provision" in a contract providing for "settle[ment] by arbitration" of "a controversy ... arising out of" that "contract ... shall be valid, irrevocable, and enforceable, save upon such grounds as exist at law or in equity for the revocation *466of any contract." 9 U.S.C. § 2. We here consider a California court's refusal to enforce an arbitration provision in a contract. In our view, that decision does not rest "upon such grounds as exist ... for the revocation of any contract," and we consequently set that judgment aside.
I
DIRECTV, Inc., the petitioner, entered into a service agreement with its customers, including respondents Amy Imburgia and Kathy Greiner. Section 9 of that contract provides that "any Claim either of us asserts will be resolved only by binding arbitration." App. 128. It then sets forth a waiver of class arbitration, stating that "[n]either you nor we shall be entitled to join or consolidate claims in arbitration." Id., at 128-129. It adds that if the "law of your state" makes the waiver of class arbitration unenforceable, then the entire arbitration provision "is unenforceable." Id., at 129. Section 10 of the contract states that § 9, the arbitration provision, "shall be governed by the Federal Arbitration Act." Ibid.
In 2008, the two respondents brought this lawsuit against DIRECTV in a California state court. They seek damages for early termination fees that they believe violate California law. After various proceedings not here relevant, DIRECTV, pointing to the arbitration provision, asked the court to send the matter to arbitration. The state trial court denied that request, and DIRECTV appealed.
The California Court of Appeal thought that the critical legal question concerned the meaning of the contractual phrase "law of your state," in this case the law of California. Does the law of California make the contract's class-arbitration waiver unenforceable? If so, as the contract provides, the entire arbitration provision is unenforceable. Or does California law permit the parties to agree to waive the right to proceed as a class in arbitration? If so, the arbitration provision is enforceable.
At one point, the law of California would have made the contract's class-arbitration waiver unenforceable. In 2005, the California Supreme Court held in Discover Bank v. Superior Court, 36 Cal.4th 148, 162-163, 30 Cal.Rptr.3d 76, 113 P.3d 1100, 1110, that a "waiver" of class arbitration in a "consumer contract of adhesion" that "predictably involve[s] small amounts of damages" and meets certain other criteria not contested here is "unconscionable under California law and should not be enforced." See Cohen v. DirecTV, Inc., 142 Cal.App.4th 1442, 1446-1447, 48 Cal.Rptr.3d 813, 815-816 (2006) (holding a class-action waiver similar to the one at issue here unenforceable pursuant to Discover Bank ); see also Consumers Legal Remedies Act, Cal. Civ.Code Ann. §§ 1751, 1781(a) (West 2009) (invalidating class-action waivers for claims brought under that statute). But in 2011, this Court held that California's Discover Bank rule " 'stands as an obstacle to the accomplishment and execution of the full purposes and objectives of Congress' " embodied in the Federal Arbitration Act. AT & T Mobility LLC v. Concepcion, 563 U.S. 333, 352, 131 S.Ct. 1740, 179 L.Ed.2d 742 (2011) (quoting Hines v. Davidowitz, 312 U.S. 52, 67, 61 S.Ct. 399, 85 L.Ed. 581 (1941) ); see Sanchez v. Valencia Holding Co., LLC, 61 Cal.4th 899, 923-924, 190 Cal.Rptr.3d 812, 353 P.3d 741, 757 (2015) (holding that Concepcion applies to the Consumers Legal Remedies Act to the extent that it would have the same effect as Discover Bank ). The Federal Arbitration Act therefore pre-empts and invalidates that rule. 563 U.S., at 352, 131 S.Ct. 1740 ; see U.S. Const., Art. VI, cl. 2.
*467The California Court of Appeal subsequently held in this case that, despite this Court's holding in Concepcion, "the law of California would find the class action waiver unenforceable." 225 Cal.App.4th 338, 342, 170 Cal.Rptr.3d 190, 194 (2014). The court noted that Discover Bank had held agreements to dispense with class-arbitration procedures unenforceable under circumstances such as these. 225 Cal.App.4th, at 341, 170 Cal.Rptr.3d, at 194. It conceded that this Court in Concepcion had held that the Federal Arbitration Act invalidated California's rule. 225 Cal.App.4th, at 341, 170 Cal.Rptr.3d, at 194. But it then concluded that this latter circumstance did not change the result-that the "class action waiver is unenforceable under California law." Id., at 347, 170 Cal.Rptr.3d, at 198.
In reaching that conclusion, the Court of Appeal referred to two sections of California's Consumers Legal Remedies Act, §§ 1751, 1781(a), rather than Discover Bank itself. See 225 Cal.App.4th, at 344, 170 Cal.Rptr.3d, at 195. Section 1751 renders invalid any waiver of the right under § 1781(a) to bring a class action for violations of that Act. The Court of Appeal thought that applying "state law alone" (that is, those two sections) would render unenforceable the class-arbitration waiver in § 9 of the contract. Id., at 344, 170 Cal.Rptr.3d, at 195. But it nonetheless recognized that if it applied federal law "then the class action waiver is enforceable and any state law to the contrary is preempted." Ibid. As far as those sections apply to class-arbitration waivers, they embody the Discover Bank rule. The California Supreme Court has recognized as much, see Sanchez, supra, at 923-924, 190 Cal.Rptr.3d 812, 353 P.3d, at 757, and no party argues to the contrary. See Supp. Brief for Respondents 2 ("The ruling in Sanchez tracks respondents' position precisely"). We shall consequently refer to the here-relevant rule as the Discover Bank rule.
The court reasoned that just as the parties were free in their contract to refer to the laws of different States or different nations, so too were they free to refer to California law as it would have been without this Court's holding invalidating the Discover Bank rule. The court thought that the parties in their contract had done just that. And it set forth two reasons for believing so.
First, § 10 of the contract, stating that the Federal Arbitration Act governs § 9 (the arbitration provision), is a general provision. But the provision voiding arbitration if the "law of your state" would find the class-arbitration waiver unenforceable is a specific provision. The court believed that the specific provision " 'is paramount to' " and must govern the general. 225 Cal.App.4th, at 344, 170 Cal.Rptr.3d, at 195 (quoting Prouty v. Gores Technology Group, 121 Cal.App.4th 1225, 1235, 18 Cal.Rptr.3d 178, 185-186 (2004) ; brackets omitted).
Second, the court said that " 'a court should construe ambiguous language against the interest of the party that drafted it.' " 225 Cal.App.4th, at 345, 170 Cal.Rptr.3d, at 196 (quoting Mastrobuono v. Shearson Lehman Hutton, Inc., 514 U.S. 52, 62, 115 S.Ct. 1212, 131 L.Ed.2d 76 (1995) ). DIRECTV had drafted the language; to void the arbitration provision was against its interest. Hence the arbitration provision was void. The Court of Appeal consequently affirmed the trial court's denial of DIRECTV's motion to enforce the arbitration provision.
The California Supreme Court denied discretionary review. App. to Pet. for Cert. 1a. DIRECTV then filed a petition for a writ of certiorari, noting that the Ninth Circuit had reached the opposite *468conclusion on precisely the same interpretive question decided by the California Court of Appeal. Murphy v. DirecTV, Inc., 724 F.3d 1218, 1226-1228 (2013). We granted the petition.
II
No one denies that lower courts must follow this Court's holding in Concepcion. The fact that Concepcion was a closely divided case, resulting in a decision from which four Justices dissented, has no bearing on that undisputed obligation. Lower court judges are certainly free to note their disagreement with a decision of this Court. But the "Supremacy Clause forbids state courts to dissociate themselves from federal law because of disagreement with its content or a refusal to recognize the superior authority of its source." Howlett v. Rose, 496 U.S. 356, 371, 110 S.Ct. 2430, 110 L.Ed.2d 332 (1990) ; cf. Khan v. State Oil Co., 93 F.3d 1358, 1363-1364 (C.A.7 1996), vacated, 522 U.S. 3, 118 S.Ct. 275, 139 L.Ed.2d 199 (1997). The Federal Arbitration Act is a law of the United States, and Concepcion is an authoritative interpretation of that Act. Consequently, the judges of every State must follow it. U.S. Const., Art. VI, cl. 2 ("[T]he Judges in every State shall be bound" by "the Laws of the United States").
While all accept this elementary point of law, that point does not resolve the issue in this case. As the Court of Appeal noted, the Federal Arbitration Act allows parties to an arbitration contract considerable latitude to choose what law governs some or all of its provisions, including the law governing enforceability of a class-arbitration waiver. 225 Cal.App.4th, at 342-343, 170 Cal.Rptr.3d, at 194. In principle, they might choose to have portions of their contract governed by the law of Tibet, the law of pre-revolutionary Russia, or (as is relevant here) the law of California including the Discover Bank rule and irrespective of that rule's invalidation in Concepcion . The Court of Appeal decided that, as a matter of contract law, the parties did mean the phrase "law of your state" to refer to this last possibility. Since the interpretation of a contract is ordinarily a matter of state law to which we defer, Volt Information Sciences, Inc. v. Board of Trustees of Leland Stanford Junior Univ., 489 U.S. 468, 474, 109 S.Ct. 1248, 103 L.Ed.2d 488 (1989), we must decide not whether its decision is a correct statement of California law but whether (assuming it is) that state law is consistent with the Federal Arbitration Act.
III
Although we may doubt that the Court of Appeal has correctly interpreted California law, we recognize that California courts are the ultimate authority on that law. While recognizing this, we must decide whether the decision of the California court places arbitration contracts "on equal footing with all other contracts." Buckeye Check Cashing, Inc. v. Cardegna, 546 U.S. 440, 443, 126 S.Ct. 1204, 163 L.Ed.2d 1038 (2006). And in doing so, we must examine whether the Court of Appeal's decision in fact rests upon "grounds as exist at law or in equity for the revocation of any contract." 9 U.S.C. § 2. That is to say, we look not to grounds that the California court might have offered but rather to those it did in fact offer. Neither this approach nor our result "steps beyond Concepcion " or any other aspect of federal arbitration law. See post, at 475 - 476 (GINSBURG, J., dissenting) (hereinafter the dissent).
We recognize, as the dissent points out, post, at 473, that when DIRECTV drafted the contract, the parties likely believed *469that the words "law of your state" included California law that then made class-arbitration waivers unenforceable. But that does not answer the legal question before us. That is because this Court subsequently held in Concepcion that the Discover Bank rule was invalid. Thus the underlying question of contract law at the time the Court of Appeal made its decision was whether the "law of your state" included invalid California law. We must now decide whether answering that question in the affirmative is consistent with the Federal Arbitration Act. After examining the grounds upon which the Court of Appeal rested its decision, we conclude that California courts would not interpret contracts other than arbitration contracts the same way. Rather, several considerations lead us to conclude that the court's interpretation of this arbitration contract is unique, restricted to that field.
First, we do not believe that the relevant contract language is ambiguous. The contract says that "[i]f ... the law of your state would find this agreement to dispense with class arbitration procedures unenforceable, then this entire Section 9 [the arbitration section] is unenforceable." App. 129. Absent any indication in the contract that this language is meant to refer to invalid state law, it presumably takes its ordinary meaning: valid state law. Indeed, neither the parties nor the dissent refer us to any contract case from California or from any other State that interprets similar language to refer to state laws authoritatively held to be invalid. While we recognize that the dissent believes this phrase to be "ambiguous," post, at 474 - 475, 475 - 476, or "anomalous," post, at 476, we cannot agree with that characterization.
Second, California case law itself clarifies any doubt about how to interpret the language. The California Supreme Court has held that under "general contract principles," references to California law incorporate the California Legislature's power to change the law retroactively. See Doe v. Harris, 57 Cal.4th 64, 69-70, 158 Cal.Rptr.3d 290, 302 P.3d 598, 601-602 (2013) (holding that plea agreements, which are governed by general contract principles, are " ' "deemed to incorporate and contemplate not only the existing law but the reserve power of the state to amend the law or enact additional laws" ' " (quoting People v. Gipson, 117 Cal.App.4th 1065, 1070, 12 Cal.Rptr.3d 478, 481 (2004) )). And judicial construction of a statute ordinarily applies retroactively. Rivers v. Roadway Express, Inc., 511 U.S. 298, 312-313, 114 S.Ct. 1510, 128 L.Ed.2d 274 (1994). As far as we are aware, the principle of California law announced in Harris, not the Court of Appeal's decision here, would ordinarily govern the scope of phrases such as "law of your state."
Third, nothing in the Court of Appeal's reasoning suggests that a California court would reach the same interpretation of "law of your state" in any context other than arbitration. The Court of Appeal did not explain why parties might generally intend the words "law of your state" to encompass "invalid law of your state." To the contrary, the contract refers to "state law" that makes the waiver of class arbitration "unenforceable," while an invalid state law would not make a contractual provision unenforceable. Assuming-as we must-that the court's reasoning is a correct statement as to the meaning of "law of your state" in this arbitration provision, we can find nothing in that opinion (nor in any other California case) suggesting that California would generally interpret words such as "law of your state" to include state laws held invalid because they conflict with, say, federal labor statutes, federal pension statutes, federal antidiscrimination *470laws, the Equal Protection Clause, or the like. Even given our assumption that the Court of Appeal's conclusion is correct, its conclusion appears to reflect the subject matter at issue here (arbitration), rather than a general principle that would apply to contracts using similar language but involving state statutes invalidated by other federal law.
Fourth, the language used by the Court of Appeal focused only on arbitration. The court asked whether "law of your state" "mean[s] 'the law of your state to the extent it is not preempted by the [Federal Arbitration Act],' or 'the law of your state without considering the preemptive effect, if any of the [Federal Arbitration Act].' " 225 Cal.App.4th, at 344, 170 Cal.Rptr.3d, at 195. Framing the question in such terms, rather than in generally applicable terms, suggests that the Court of Appeal could well have meant that its holding was limited to the specific subject matter of this contract-arbitration.
Fifth, the Court of Appeal reasoned that invalid state arbitration law, namely the Discover Bank rule, maintained legal force despite this Court's holding in Concepcion . The court stated that "[i]f we apply state law alone ... to the class action waiver, then the waiver is unenforceable." 225 Cal.App.4th, at 344, 170 Cal.Rptr.3d, at 195. And at the end of its opinion it reiterated that "[t]he class action waiver is unenforceable under California law, so the entire arbitration agreement is unenforceable." Id., at 347, 170 Cal.Rptr.3d, at 198. But those statements do not describe California law. See Concepcion, 563 U.S., at 344, 352, 131 S.Ct. 1740 ; Sanchez, 61 Cal.4th, at 923-924, 190 Cal.Rptr.3d 812, 353 P.3d, at 757. The view that state law retains independent force even after it has been authoritatively invalidated by this Court is one courts are unlikely to accept as a general matter and to apply in other contexts.
Sixth, there is no other principle invoked by the Court of Appeal that suggests that California courts would reach the same interpretation of the words "law of your state" in other contexts. The court said that the phrase "law of your state" constitutes " 'a specific exception ' " to the agreement's " 'general adoption of the [Federal Arbitration Act].' " 225 Cal.App.4th, at 344, 170 Cal.Rptr.3d, at 195. But that tells us nothing about how to interpret the words "law of your state" elsewhere. It does not answer the relevant question: whether those words encompass laws that have been authoritatively held invalid. Cf. Prouty, 121 Cal.App.4th, at 1235, 18 Cal.Rptr.3d, at 185-186 (specific words govern only "when a general and a particular provision are inconsistent").
The court added that it would interpret " 'ambiguous language against the interest of the party that drafted it,' " namely DIRECTV. 225 Cal.App.4th, at 345, 170 Cal.Rptr.3d, at 196 (quoting Mastrobuono, 514 U.S., at 62, 115 S.Ct. 1212 ). The dissent adopts a similar argument. See post, at 474 - 476. But, as we have pointed out, supra, at 469 - 470, were the phrase "law of your state" ambiguous, surely some court would have construed that term to incorporate state laws invalidated by, for example, federal labor law, federal pension law, or federal civil rights law. Yet, we have found no such case. Moreover, the reach of the canon construing contract language against the drafter must have limits, no matter who the drafter was. The fact that we can find no similar case interpreting the words "law of your state" to include invalid state laws indicates, at the least, that the antidrafter canon would not lead California courts to *471reach a similar conclusion in similar cases that do not involve arbitration.
* * *
Taking these considerations together, we reach a conclusion that, in our view, falls well within the confines of (and goes no further than) present well-established law. California's interpretation of the phrase "law of your state" does not place arbitration contracts "on equal footing with all other contracts," Buckeye Check Cashing, Inc., 546 U.S., at 443, 126 S.Ct. 1204. For that reason, it does not give "due regard ... to the federal policy favoring arbitration." Volt Information Sciences, 489 U.S., at 476, 109 S.Ct. 1248. Thus, the Court of Appeal's interpretation is pre-empted by the Federal Arbitration Act. See Perry v. Thomas, 482 U.S. 483, 493, n. 9, 107 S.Ct. 2520, 96 L.Ed.2d 426 (1987) (noting that the Federal Arbitration Act pre-empts decisions that take their "meaning precisely from the fact that a contract to arbitrate is at issue"). Hence, the California Court of Appeal must "enforc[e]" the arbitration agreement. 9 U.S.C. § 2.
The judgment of the California Court of Appeal is reversed, and the case is remanded for further proceedings not inconsistent with this opinion.
It is so ordered.