Human verbal communication includes affective messages which are conveyed through use of emotionally colored words. There has been a lot of research in this direction but the problem of integrating state-of-the-art neural language models with affective information remains an area ripe for exploration. In this paper, we propose an extension to an LSTM (Long Short-Term Memory) language model for generating conversational text, conditioned on affect categories. Our proposed model, Affect-LM enables us to customize the degree of emotional content in generated sentences through an additional design parameter. Perception studies conducted using Amazon Mechanical Turk show that Affect-LM generates naturally looking emotional sentences without sacrificing grammatical correctness. Affect-LM also learns affect-discriminative word representations, and perplexity experiments show that additional affective information in conversational text can improve language model prediction.