We propose a supervised maximum entropy ranking approach to pronoun resolution as an alternative to commonly used classification-based approaches. Classification approaches consider only one or two candidate antecedents for a pronoun at a time, whereas ranking allows all candidates to be evaluated together. We argue that this provides a more natural fit for the task than classification and show that it delivers significant performance improvements on the ACE datasets. In particular, our ranker obtains an error reduction of 9.7% over the best classification approach, the twin-candidate model. Furthermore, we show that the ranker offers some computational advantage over the twincandidate classifier, since it easily allows the inclusion of more candidate antecedents during training. This approach leads to a further error reduction of 5.4% (a total reduction of 14.6% over the twincandidate model).