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Large Language Models (LLMs) have demonstrated impressive planning abilities in single-agent embodied tasks across various domains. However, their capacity for planning and communication in multi-agent cooperation remains unclear, even though these are crucial skills for intelligent embodied agents. In this paper, we present a novel framework that utilizes LLMs for multi-agent cooperation and tests it in various embodied environments. Our framework enables embodied agents to plan, communicate, and cooperate with other embodied agents or humans to accomplish long-horizon tasks efficiently. We demonstrate that recent LLMs, such as GPT-4, can surpass strong planning-based methods and exhibit emergent effective communication using our framework without requiring fine-tuning or few-shot prompting. We also discover that LLM-based agents that communicate in natural language can earn more trust and cooperate more effectively with humans. Our research underscores the potential of LLMs for embodied AI and lays the foundation for future research in multi-agent cooperation. Videos can be found on the project's website.