We introduce MuseChat, an innovative dialog-based music recommendation system. This unique platform not only offers interactive user engagement but also suggests music tailored for input videos, so that users can refine and personalize their music selections. In contrast, previous systems predominantly emphasized content compatibility, often overlooking the nuances of users' individual preferences. For example, all the datasets only provide basic music-video pairings or such pairings with textual music descriptions. To address this gap, our research offers three contributions. First, we devise a conversation-synthesis method that simulates a two-turn interaction between a user and a recommendation system, which leverages pre-trained music tags and artist information. In this interaction, users submit a video to the system, which then suggests a suitable music piece with a rationale. Afterwards, users communicate their musical preferences, and the system presents a refined music recommendation with reasoning. Second, we introduce a multi-modal recommendation engine that matches music either by aligning it with visual cues from the video or by harmonizing visual information, feedback from previously recommended music, and the user's textual input. Third, we bridge music representations and textual data with a Large Language Model(Vicuna-7B). This alignment equips MuseChat to deliver music recommendations and their underlying reasoning in a manner resembling human communication. Our evaluations show that MuseChat surpasses existing state-of-the-art models in music retrieval tasks and pioneers the integration of the recommendation process within a natural language framework.