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In this paper, I introduce a Bayesian model for detecting changepoints in a time series of overdispersed counts, such as contributions to candidates over the course of a campaign or counts of terrorist violence. To avoid having to specify the number of changepoint ex ante, this model incorporates a hierarchical Dirichlet process prior to estimate the number of changepoints as well as their location. This allows researchers to discover salient structural breaks and perform inference on the number of such breaks in a given time series. I demonstrate the usefulness of the model with applications to campaign contributions in the 2012 U.S. Republican presidential primary and incidences of global terrorism from 1970 to 2015.