Large Language Model (LLM) agents are increasingly used in many applications, raising concerns about their safety. While previous work has shown that LLMs can deceive in controlled tasks, less is known about their ability to deceive using natural language in social contexts. In this paper, we study deception in the Social Deduction Game (SDG) Mafia, where success is dependent on deceiving others through conversation. Unlike previous SDG studies, we use an asynchronous multi-agent framework which better simulates realistic social contexts. We simulate 35 Mafia games with GPT-4o LLM agents. We then create a Mafia Detector using GPT-4-Turbo to analyze game transcripts without player role information to predict the mafia players. We use prediction accuracy as a surrogate marker for deception quality. We compare this prediction accuracy to that of 28 human games and a random baseline. Results show that the Mafia Detector's mafia prediction accuracy is lower on LLM games than on human games. The result is consistent regardless of the game days and the number of mafias detected. This indicates that LLMs blend in better and thus deceive more effectively. We also release a dataset of LLM Mafia transcripts to support future research. Our findings underscore both the sophistication and risks of LLM deception in social contexts.