This paper describes an efficient sampler for synchronous grammar induction under a nonparametric Bayesian prior. Inspired by ideas from slice sampling, our sampler is able to draw samples from the posterior distributions of models for which the standard dynamic programing based sampler proves intractable on non-trivial corpora. We compare our sampler to a previously proposed Gibbs sampler and demonstrate strong improvements in terms of both training log-likelihood and performance on an end-to-end translation evaluation.