||We introduce a stochastic grammatical channel model for machine translation, that synthesizes several desirable characteristics of both statistical and grammatical machine translation. As with the pure statistical translation model described by Wu (1996) (in which a bracketing transduction grammar models the channel), alternative hypotheses compete probabilistically, exhaustive search of the translation hypothesis space can be performed in polynomial time, and robustness heuristics arise naturally from a language-independent inversion-transduction model. However, unlike pure statistical translation models, the generated output string is guaranteed to conform to a given target grammar. The model employs only (1) a translation lexicon, (2) a context-free grammar for the target language, and (3) a bigram language model. The fact that no explicit bilingual translation rules are used makes the model easily portable to a variety of source languages. Experiments show that it also achieves significant speed gains over our earlier model.