We study whether large language models (LLMs) can predict human strategic behavior from pre-play communication. Using three canonical laboratory games that vary in incentive alignment and communication structure, we provide LLMs and incentivized human forecasters with identical transcripts and ask them to predict players' subsequent actions. Using GPT-5 as our main model, we find that it consistently outperforms humans and achieves accuracy well above chance, especially when incentives are aligned and communication is bilateral. The performance gap arises almost entirely from correctly forecasting cooperative actions, while both humans and GPT--5 struggle to anticipate defection. These results suggest that strategic communication contains systematic information about future behavior that humans underutilize and that LLMs are able to exploit more effectively.