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Speech recognition systems have historically used contextdependent phones as acoustic units because these units allow linguistic information, such as a pronunciation lexicon, to be leveraged. However, when dealing with a new language for which minimal linguistic resources exist, it is desirable to automatically discover acoustic units. The process of discovering acoustic units usually consists of two stages: segmentation and clustering. In this paper, we focus on the segmentation portion of this problem. We introduce a nonparametric Bayesian approach for segmentation, based on Hierarchical Dirichlet Processes (HDP), in which a hidden Markov model (HMM) with an unbounded number of states is used to segment the utterance. This model is referred to as an HDP-HMM. We compare this algorithm to several popular heuristic methods and demonstrate an 11% improvement in finding boundaries on the TIMIT Corpus. A self-similarity measure over segments shows an 88% improvement compared to manual segmentation with comparable segment length. This work represents the first step in the development of a speech recognition system that is entirely based on nonparametric Bayesian models.