Recent works in neural machine translation have begun to explore document translation. However, translating online multi-speaker conversations is still an open problem. In this work, we propose the task of translating Bilingual Multi-Speaker Conversations, and explore neural architectures which exploit both source and target-side conversation histories for this task. To initiate an evaluation for this task, we introduce datasets extracted from Europarl v7 and OpenSubtitles2016. Our experiments on four language-pairs confirm the significance of leveraging conversation history, both in terms of BLEU and manual evaluation.