To scale non-parametric extensions of probabilistic topic models such as Latent Dirichlet allocation to larger data sets, practitioners rely increasingly on parallel and distributed systems. In this work, we study data-parallel training for the hierarchical Dirichlet process (HDP) topic model. Based upon a representation of certain conditional distributions within an HDP, we propose a doubly sparse data-parallel sampler for the HDP topic model. This sampler utilizes all available sources of sparsity found in natural language - an important way to make computation efficient. We benchmark our method on a well-known corpus (PubMed) with 8m documents and 768m tokens, using a single multi-core machine in under four days.