It has been frequently observed that human speakers align their language use with each other during conversations. In this paper, we study empirically whether large language models (LLMs) exhibit the same behavior of conversational adaptation.We construct a corpus of conversations between LLMs and find that two LLM agents end up making more similar syntactic choices as conversations go on, confirming that modern LLMs adapt their language use to their conversational partners in at least a rudimentary way.