Since its launch in November 2022, ChatGPT has gained popularity among users, especially programmers who use it to solve development issues. However, while offering a practical solution to programming problems, ChatGPT should be used primarily as a supporting tool (e.g., in software education) rather than as a replacement for humans. Thus, detecting automatically generated source code by ChatGPT is necessary, and tools for identifying AI-generated content need to be adapted to work effectively with code. This paper presents GPTSniffer–a novel approach to the detection of source code written by AI–built on top of CodeBERT. We conducted an empirical study to investigate the feasibility of automated identification of AI-generated code, and the factors that influence this ability. The results show that GPTSniffer can accurately classify whether code is human-written or AI-generated, outperforming two baselines, GPTZero and OpenAI Text Classifier. Also, the study shows how similar training data or a classification context with paired snippets helps boost the prediction. We conclude that GPTSniffer can be leveraged in different contexts, e.g., in software engineering education, where teachers use the tool to detect cheating and plagiarism, or in development, where AI-generated code may require peculiar quality assurance activities.