We propose the first unsupervised approach to the problem of modeling dialogue acts in an open domain. Trained on a corpus of noisy Twitter conversations, our method discovers dialogue acts by clustering raw utterances. Because it accounts for the sequential behaviour of these acts, the learned model can provide insight into the shape of communication in a new medium. We address the challenge of evaluating the emergent model with a qualitative visualization and an intrinsic conversation ordering task. This work is inspired by a corpus of 1.3 million Twitter conversations, which will be made publicly available. This huge amount of data, available only because Twitter blurs the line between chatting and publishing, highlights the need to be able to adapt quickly to a new medium.