Tree based translation models are a compelling means of integrating linguistic information into machine translation. Syntax can inform lexical selection and reordering choices and thereby improve translation quality. Research to date has focussed primarily on decoding with such models, but less on the difficult problem of inducing the bilingual grammar from data. We propose a generative Bayesian model of tree-to-string translation which induces grammars that are both smaller and produce better translations than the previous heuristic two-stage approach which employs a separate word alignment step.