Conversational Question Answering over Knowledge Graphs (KGs) combines the factual grounding of KG-based QA with the interactive nature of dialogue systems. KGs are widely used in enterprise and domain applications to provide structured, evolving, and reliable knowledge. Large language models (LLMs) enable natural and context-aware conversations, but lack direct access to private and dynamic KGs. Retrieval-augmented generation (RAG) systems can retrieve graph content but often serialize structure, struggle with multi-turn context, and require heavy indexing. Traditional KGQA systems preserve structure but typically support only single-turn QA, incur high latency, and struggle with coreference and context tracking. To address these limitations, we propose Chatty-KG, a modular multi-agent system for conversational QA over KGs. Chatty-KG combines RAG-style retrieval with structured execution by generating SPARQL queries through task-specialized LLM agents. These agents collaborate for contextual interpretation, dialogue tracking, entity and relation linking, and efficient query planning, enabling accurate and low-latency translation of natural questions into executable queries. Experiments on large and diverse KGs show that Chatty-KG significantly outperforms state-of-the-art baselines in both single-turn and multi-turn settings, achieving higher F1 and P@1 scores. Its modular design preserves dialogue coherence and supports evolving KGs without fine-tuning or pre-processing. Evaluations with commercial (e.g., GPT-4o, Gemini-2.0) and open-weight (e.g., Phi-4, Gemma 3) LLMs confirm broad compatibility and stable performance. Overall, Chatty-KG unifies conversational flexibility with structured KG grounding, offering a scalable and extensible approach for reliable multi-turn KGQA.