People's reactions to coincidences are often cited as an illustration of the irrationality of human reasoning about chance. We argue that coincidences may be better understood in terms of rational statistical inference, based on their functional role in processes of causal discovery and theory revision. We present a formal definition of coincidences in the context of a Bayesian framework for causal induction: a coincidence is an event that provides support for an alternative to a currently favored causal theory, but not necessarily enough support to accept that alternative in light of its low prior probability. We test the qualitative and quantitative predictions of this account through a series of experiments that examine the transition from coincidence to evidence, the correspondence between the strength of coincidences and the statistical support for causal structure, and the relationship between causes and coincidences. Our results indicate that people can accurately assess the strength of coincidences, suggesting that irrational conclusions drawn from coincidences are the consequence of overestimation of the plausibility of novel causal forces. We discuss the implications of our account for understanding the role of coincidences in theory change.