Modern distributed data management systems face a new challenge: how can autonomous, mutually-distrusting parties cooperate safely and effectively? Addressing this challenge brings up questions familiar from classical distributed systems: how to combine multiple steps into a single atomic action, how to recover from failures, and how to synchronize concurrent access to data. Nevertheless, each of these issues requires rethinking when participants are autonomous and potentially adversarial. We propose the notion of a *cross-chain deal*, a new way to structure complex distributed computations that manage assets in an adversarial setting. Deals are inspired by classical atomic transactions, but are necessarily different, in important ways, to accommodate the decentralized and untrusting nature of the exchange. We describe novel safety and liveness properties, along with two alternative protocols for implementing cross-chain deals in a system of independent blockchain ledgers. One protocol, based on synchronous communication, is fully decentralized, while the other, based on semi-synchronous communication, requires a globally shared ledger.