In software development, resolving the emergent issues within GitHub repositories is a complex challenge that involves not only the incorporation of new code but also the maintenance of existing code. Large Language Models (LLMs) have shown promise in code generation but face difficulties in resolving Github issues, particularly at the repository level. To overcome this challenge, we empirically study the reason why LLMs fail to resolve GitHub issues and analyze the major factors. Motivated by the empirical findings, we propose a novel LLM-based Multi-Agent framework for GitHub Issue reSolution, MAGIS, consisting of four agents customized for software evolution: Manager, Repository Custodian, Developer, and Quality Assurance Engineer agents. This framework leverages the collaboration of various agents in the planning and coding process to unlock the potential of LLMs to resolve GitHub issues. In experiments, we employ the SWE-bench benchmark to compare MAGIS with popular LLMs, including GPT-3.5, GPT-4, and Claude-2. MAGIS can resolve 13.94% GitHub issues, significantly outperforming the baselines. Specifically, MAGIS achieves an eight-fold increase in resolved ratio over the direct application of GPT-4, the advanced LLM.