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We introduce a protocol for schema evolution in a globally distributed database management system with shared data, stateless servers, and no global membership. Our protocol is asynchronous--it allows different servers in the database system to transition to a new schema at different times--and online--all servers can access and update all data during a schema change. We provide a formal model for determining the correctness of schema changes under these conditions, and we demonstrate that many common schema changes can cause anomalies and database corruption. We avoid these problems by replacing corruption-causing schema changes with a sequence of schema changes that is guaranteed to avoid corrupting the database so long as all servers are no more than one schema version behind at any time. Finally, we discuss a practical implementation of our protocol in F1, the database management system that stores data for Google AdWords.