Despite continuous advancements in deep learning for understanding human motion, existing models often struggle to accurately identify action timing and specific body parts, typically supporting only single-round interaction. Such limitations in capturing fine-grained motion details reduce their effectiveness in motion understanding tasks. In this paper, we propose MoChat, a multimodal large language model capable of spatio-temporal grounding of human motion and understanding multi-turn dialogue context. To achieve these capabilities, we group the spatial information of each skeleton frame based on human anatomical structure and then apply them with Joints-Grouped Skeleton Encoder, whose outputs are combined with LLM embeddings to create spatio-aware and temporal-aware embeddings separately. Additionally, we develop a pipeline for extracting timestamps from skeleton sequences based on textual annotations, and construct multi-turn dialogues for spatially grounding. Finally, various task instructions are generated for jointly training. Experimental results demonstrate that MoChat achieves state-of-the-art performance across multiple metrics in motion understanding tasks, making it as the first model capable of fine-grained spatio-temporal grounding of human motion.