We present a probabilistic approach to learning to interpret temporal phrases given only a corpus of utterances and the times they reference. While most approaches to the task have used regular expressions and similar linear pattern interpretation rules, the possibility of phrasal embedding and modification in time expressions motivates our use of a compositional grammar of time expressions. This grammar is used to construct a latent parse which evaluates to the time the phrase would represent, as a logical parse might evaluate to a concrete entity. In this way, we can employ a loosely supervised EM-style bootstrapping approach to learn these latent parses while capturing both syntactic uncertainty and pragmatic ambiguity in a probabilistic framework. We achieve an accuracy of 72% on an adapted TempEval-2 task – comparable to state of the art systems.