For decades, the Supreme Court has expanded the Federal Arbitration Act (FAA) and companies have placed arbitration clauses in hundreds of millions of contracts. This Article examines a less‐obvious way in which arbitration’s tendrils are growing. Once, even the broadest arbitration provisions only governed allegations that were somehow connected to the agreement between the parties (the “container contract”). As a result, they often did not cover shocking and unforeseeable misconduct, or parties who did not sign the container contract, or claims that arose after the agreement lapsed. But now businesses are experimenting with what this Article calls “infinite” arbitration clauses: those that mandate arbitration for all disputes between any related party in perpetuity. Moreover, to cut courts out of the loop, drafters are coupling infinite provisions with so‐called “delegation” clauses, which give the arbitrator the exclusive right to determine whether to send a cause of action to arbitration.