Zero-shot keyphrase extraction aims to build a keyphrase extractor without training by human-annotated data, which is challenging due to the limited human intervention involved. Challenging but worthwhile, zero-shot setting efficiently reduces the time and effort that data labeling takes. Recent efforts on pre-trained large language models (e.g., ChatGPT and ChatGLM) show promising performance on zero-shot settings, thus inspiring us to explore prompt-based methods. In this paper, we ask whether strong keyphrase extraction models can be constructed by directly prompting the large language model ChatGPT. Through experimental results, it is found that ChatGPT still has a lot of room for improvement in the keyphrase extraction task compared to existing state-of-the-art unsupervised and supervised models.