Since its launch in November 2022, ChatGPT has gained popularity among users, especially programmers who use it as a tool to solve development problems. However, while offering a practical solution to programming problems, ChatGPT should be mainly used as a supporting tool (e.g., in software education) rather than as a replacement for the human being. Thus, detecting automatically generated source code by ChatGPT is necessary, and tools for identifying AI-generated content may need to be adapted to work effectively with source code. This paper presents an empirical study to investigate the feasibility of automated identification of AI-generated code snippets, and the factors that influence this ability. To this end, we propose a novel approach called GPTSniffer, which builds on top of CodeBERT to detect source code written by AI. The results show that GPTSniffer can accurately classify whether code is human-written or AI-generated, and outperforms two baselines, GPTZero and OpenAI Text Classifier. Also, the study shows how similar training data or a classification context with paired snippets helps to boost classification performances.