Event extraction systems typically locate the role fillers for an event by analyzing sentences in isolation and identifying each role filler independently of the others. We argue that more accurate event extraction requires a view of the larger context to decide whether an entity is related to a relevant event. We propose a bottom-up approach to event extraction that initially identifies candidate role fillers independently and then uses that information as well as discourse properties to model textual cohesion. The novel component of the architecture is a sequentially structured sentence classifier that identifies event-related story contexts. The sentence classifier uses lexical associations and discourse relations across sentences, as well as domain-specific distributions of candidate role fillers within and across sentences. This approach yields state-of-the-art performance on the MUC-4 data set, achieving substantially higher precision than previous systems.