Despite providing superior performance, open-source large language models (LLMs) are vulnerable to abusive usage. To address this issue, recent works propose LLM fingerprinting methods to identify the specific source LLMs behind suspect applications. However, these methods fail to provide stealthy and robust fingerprint verification. In this paper, we propose a novel LLM fingerprinting scheme, namely CoTSRF, which utilizes the Chain of Thought (CoT) as the fingerprint of an LLM. CoTSRF first collects the responses from the source LLM by querying it with crafted CoT queries. Then, it applies contrastive learning to train a CoT extractor that extracts the CoT feature (i.e., fingerprint) from the responses. Finally, CoTSRF conducts fingerprint verification by comparing the Kullback-Leibler divergence between the CoT features of the source and suspect LLMs against an empirical threshold. Various experiments have been conducted to demonstrate the advantage of our proposed CoTSRF for fingerprinting LLMs, particularly in stealthy and robust fingerprint verification.