Community finding in social network analysis is the task of identifying groups of people within a larger population who are more likely to connect to each other than connect to others in the population. Much existing research has focussed on non-overlapping clustering. However, communities in real world social networks do overlap. This paper introduces a new community finding method based on overlapping clustering. A Bayesian statistical model is presented, and a Markov Chain Monte Carlo (MCMC) algorithm is presented and evaluated in comparison with two existing overlapping community finding methods that are applicable to large networks. We evaluate our algorithm on networks with thousands of nodes and tens of thousands of edges.