We present a data-driven approach to generating responses to Twitter status posts, based on phrase-based Statistical Machine Translation. We find that mapping conversational stimuli onto responses is more difficult than translating between languages, due to the wider range of possible responses, the larger fraction of unaligned words/phrases, and the presence of large phrase pairs whose alignment cannot be further decomposed. After addressing these challenges, we compare approaches based on SMT and Information Retrieval in a human evaluation. We show that SMT outperforms IR on this task, and its output is preferred over actual human responses in 15% of cases. As far as we are aware, this is the first work to investigate the use of phrase-based SMT to directly translate a linguistic stimulus into an appropriate response.