Language is fundamentally generative, allowing us to construct a potentially infinite variety of utterances. It is generativity commonly held to be unique to humans, but I argue instead that it is a characteristic of thought, with origins far back in evolution. It may derive fundamentally from mental time travel, the capacity to imagine past and possible future episodes, and even invent purely imaginary ones. Some have argued that mental time travel is also unique to humans, but I review evidence that it has a long evolutionary history. Behavioral evidence suggests that a wide range of species can imagine past episodes and plan future ones. Neurophysiological evidence from rodents and neuropsychology and brain imaging in humans point to a critical role for the hippocampus and entorhinal cortex in the “replay” of past episodes and the “preplay” of possible future ones. Language emerged as a device for sharing mental travels in time and place, originating in bodily gesture, but becoming more abstract through conventionalization, with vocal gestures augmenting and eventually largely replacing manual ones. The generativity of language derives, not from language itself, but from the underlying thoughts that language expresses.