A program is reentrant if distinct executions of that program on distinct inputs cannot affect each other. Reentrant programs have the desirable property that they can be deployed on parallel machines without additional concurrency control. Many existing Java programs are not reentrant because they rely on mutable global state. We present a refactoring that makes such programs reentrant by replacing global state with thread-local state and performing each execution in a fresh thread. The approach has the key advantage of yielding a program that is obviously safe for parallel execution; the program can then be optimized selectively for better performance. We implemented this refactoring in Reentrancer, a practical Eclipse-based tool. Reentrancer successfully eliminated observed reentrancy problems in several single-threaded Java benchmarks. For three of these benchmarks, Reentrancer enabled speedups on a multicore machine without any further code modification.