We present a probabilistic formulation to max-margin matrix factorization and build accordingly an infinite nonparametric Bayesian model to automatically resolve the unknown number of latent factors. Our work demonstrates a successful example that integrates Bayesian nonparametrics and max-margin learning, which are conventionally two separate paradigms and enjoy complementary advantages. We develop an efficient variational learning algorithm for posterior inference, and our extensive empirical studies on large-scale MovieLens and EachMovie data sets appear to demonstrate the advantages inherited from both max-margin matrix factorization and Bayesian nonparametrics.