When multiple conversations occur simultaneously, a listener must decide which conversation each utterance is part of in order to interpret and respond to it appropriately. We refer to this task as disentanglement. We present a corpus of Internet Relay Chat dialogue in which the various conversations have been manually disentangled, and evaluate annotator reliability. We propose a graph-based clustering model for disentanglement, using lexical, timing, and discourse-based features. The model's predicted disentanglements are highly correlated with manual annotations. We conclude by discussing two extensions to the model, specificity tuning and conversation start detection, both of which are promising but do not currently yield practical improvements.