Multimodal machine translation and textual chat translation have received considerable attention in recent years. Although the conversation in its natural form is usually multimodal, there still lacks work on multimodal machine translation in conversations. In this work, we introduce a new task named Multimodal Chat Translation (MCT), aiming to generate more accurate translations with the help of the associated dialogue history and visual context. To this end, we firstly construct a Multimodal Sentiment Chat Translation Dataset (MSCTD) containing 142,871 English-Chinese utterance pairs in 14,762 bilingual dialogues and 30,370 English-German utterance pairs in 3,079 bilingual dialogues. Each utterance pair, corresponding to the visual context that reflects the current conversational scene, is annotated with a sentiment label. Then, we benchmark the task by establishing multiple baseline systems that incorporate multimodal and sentiment features for MCT. Preliminary experiments on four language directions (English-Chinese and English-German) verify the potential of contextual and multimodal information fusion and the positive impact of sentiment on the MCT task. Additionally, as a by-product of the MSCTD, it also provides two new benchmarks on multimodal dialogue sentiment analysis. Our work can facilitate research on both multimodal chat translation and multimodal dialogue sentiment analysis.