The capacity to generate a limitless range of meaningful expressions from a finite set of elements differentiates human language from other animal communication systems. Rule systems capable of generating an infinite set of outputs ("grammars") vary in generative power. The weakest possess only local organizational principles, with regularities limited to neighboring units. We used a familiarization/discrimination paradigm to demonstrate that monkeys can spontaneously master such grammars. However, human language entails more sophisticated grammars, incorporating hierarchical structure. Monkeys tested with the same methods, syllables, and sequence lengths were unable to master a grammar at this higher, "phrase structure grammar" level.