Conversation is an essential component of social behaviour, one of the primary means by which humans express emotions, moods, attitudes and personality. Thus a key technical capability for dialogue applications, such as interactive narrative systems, human robot interaction and spoken dialogue systems, is the ability to support natural conversational interaction. However, system utterances in existing systems are typically handcrafted, leading to problems of portability and scalability. We propose a framework for automatically generating language projecting different personality traits based on the 'Big Five' model of personality. We show that our PERSONAGE generator can produce utterances with recognisable personality for all Big Five traits, according to human judges. We also test the ability of PERSONAGE to vary the characters' personality in an existing interactive narrative system, showing that some forms of variation can be automatically obtained in a new domain, depending on the level of utterance representation.