This case originated as a garden-variety, state-law-based contract action: Discover sued its cardholder, [Betty] Vaden, in a Maryland state court to recover arrearages amounting to $10,610.74, plus interest and counsel fees. [Court’s footnote: Discover apparently had no access to a federal forum for its suit against Vaden on the basis of diversity-of-citizenship jurisdiction. Under that head of federal-court jurisdiction, the amount in controversy must ‘‘excee[d] … $75,000.’’] Vaden’s answer asserted usury as an affirmative defense. Vaden also filed several counterclaims, styled as class actions. Like Discover’s complaint, Vaden’s pleadings invoked only state law: Vaden asserted that Discover’s demands for finance charges, interest, and late fees violated Maryland’s credit laws. [Citation.] Neither party invoked—by notice to the other or petition to the state court—the clause in the credit card agreement providing for arbitration of ‘‘any claim or dispute between [Discover and Vaden].’’ [Citation.]

   Faced with Vaden’s counterclaims, Discover sought federal- court aid. It petitioned the United States District Court for the District of Maryland for an order, pursuant to § 4 of the Federal Arbitration Act (FAA or Act), [citation], compelling arbitration of Vaden’s counterclaims. Although those counterclaims were framed under state law, Discover urged that they were governed entirely by federal law, specifically, § 27(a) of the Federal Deposit Insurance Act (FDIA), [citation], prescribes the interest rates state-chartered, federally insured banks like Discover can charge, ‘‘notwithstanding any State constitution or statute which is hereby preempted.’’ This provision, Discover maintained, was completely preemptive, i.e., it superseded otherwise applicable Maryland law, and placed Vaden’s counterclaims under the exclusive governance of the FDIA. On that basis, Discover asserted, the District Court had authority to entertain the § 4 petition pursuant to [citation], which gives federal courts jurisdiction over cases ‘‘arising under’’ federal law.

   [The District Court agreed and ordered arbitration. Reasoning that a Federal court has jurisdiction over a § 4 petition if the parties’ underlying dispute presents a Federal question, the Fourth Circuit eventually affirmed. Vaden sought review by the U.S. Supreme Court, which granted certiorari.]

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   In 1925, Congress enacted the FAA [Federal Arbitration Act] ‘‘[t]o overcome judicial resistance to arbitration,’’ [citation], and to declare ‘‘‘a national policy favoring arbitration’ of claims that parties contract to settle in that manner,’’ [citation]. To that end, § 2 provides that arbitration agreements in contracts ‘‘involving commerce’’ are ‘‘valid, irrevocable, and enforceable.’’ [Citation.] Section 4—the section at issue here—provides for United States district court enforcement of arbitration agreements. Petitions to compel arbitration, § 4 states, may be brought before ‘‘any United States district court which, save for such agreement, would have jurisdiction under title 28 [of the U.S. Code] of the subject matter of a suit arising out of the controversy between the parties.’’ [Citation.]

   The ‘‘body of federal substantive law’’ generated by elaboration of FAA § 2 is equally binding on state and federal courts. [Citations.] ‘‘As for jurisdiction over controversies touching arbitration,’’ however, the Act is ‘‘something of an anomaly’’ in the realm of federal legislation: It ‘‘bestow[s] no federal jurisdiction but rather requir[es] [for access to a federal forum] an independent jurisdictional basis’’ over the parties’ dispute. [Citation.] * * *

   The independent jurisdictional basis Discover relies upon in this case is 28 U.S.C. § 1331, which vests in federal district courts jurisdiction over ‘‘all civil actions arising under the Constitution, laws, or treaties of the United States.’’ Under the longstanding well-pleaded complaint rule, however, a suit ‘‘arises under’’ federal law ‘‘only when the plaintiff’s statement of his own cause of action shows that it is based upon [federal law].’’ [Citation.] Federal jurisdiction cannot be predicated on an actual or anticipated defense: ‘‘It is not enough that the plaintiff alleges some anticipated defense to his cause of action and asserts that the defense is invalidated by some provision of [federal law].’’ [Citation.]

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   A complaint purporting to rest on state law, we have recognized, can be recharacterized as one ‘‘arising under’’ federal law if the law governing the complaint is exclusively federal. [Citation.] Under this so-called ‘‘complete preemption doctrine,’’ a plaintiff’s ‘‘state cause of action [may be recast] as a federal claim for relief, making [its] removal [by the defendant] proper on the basis of federal question jurisdiction.’’ [Citation.] A state-law-based counterclaim, however, even if similarly susceptible to recharacterization, would remain nonremovable. Under our precedent construing § 1331, as just explained, counterclaims, even if they rely exclusively on federal substantive law, do not qualify a case for federal-court cognizance.

   Attending to the language of the FAA and the above described jurisdictional tenets, we approve the ‘‘look through’’ approach to this extent: A federal court may ‘‘look through’’ a § 4 petition to determine whether it is predicated on an action that ‘‘arises under’’ federal law; in keeping with the well-pleaded complaint rule as amplified in [citation] however, a federal court may not entertain a § 4 petition based on the contents, actual or hypothetical, of a counterclaim.

   The text of § 4 drives our conclusion that a federal court should determine its jurisdiction by ‘‘looking through’’ a § 4 petition to the parties’ underlying substantive controversy.

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   The phrase ‘‘save for [the arbitration] agreement’’ indicates that the district court should assume the absence of the arbitration agreement and determine whether it ‘‘would have jurisdiction under title 28’’ without it. [Citation.] * * *

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   Having determined that a district court should ‘‘look through’’ a § 4 petition, we now consider whether the court ‘‘would have [federal-question] jurisdiction’’ over ‘‘a suit arising out of the controversy’’ between Discover and Vaden. [Citation.] As explained above, § 4 of the FAA does not enlarge federal-court jurisdiction; rather, it confines federal courts to the jurisdiction they would have ‘‘save for [the arbitration] agreement.’’ [Citation.] Mindful of that limitation, we read § 4 to convey that a party seeking to compel arbitration may gain a federal court’s assistance only if, ‘‘save for’’ the agreement, the entire, actual ‘‘controversy between the parties,’’ as they have framed it, could be litigated in federal court. We conclude that the parties’ actual controversy, here precipitated by Discover’s state-court suit for the balance due on Vaden’s account, is not amenable to federal-court adjudication. Consequently, the § 4 petition Discover filed in the United States District Court for the District of Maryland must be dismissed.

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   Discover, we note, is not left without recourse. Under the FAA, state courts as well as federal courts are obliged to honor and enforce agreements to arbitrate. [Citations.] Discover may therefore petition a Maryland court for aid in enforcing the arbitration clause of its contracts with Maryland cardholders.

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   For the reasons stated, the District Court lacked jurisdiction to entertain Discover’s § 4 petition to compel arbitration. The judgment of the Court of Appeals affirming the District Court’s order is therefore reversed, and the case is remanded for further proceedings consistent with this opinion.