Open-domain dialog systems (also known as chatbots) have increasingly drawn attention in natural language processing. Some of the recent work aims at incorporating affect information into sequence-to-sequence neural dialog modeling, making the response emotionally richer, while others use hand-crafted rules to determine the desired emotion response. However, they do not explicitly learn the subtle emotional interactions captured in human dialogs. In this paper, we propose a multi-turn dialog system aimed at learning and generating emotional responses that so far only humans know how to do. Compared with two baseline models, offline experiments show that our method performs the best in perplexity scores. Further human evaluations confirm that our chatbot can keep track of the conversation context and generate emotionally more appropriate responses while performing equally well on grammar.