Large language models (LLMs) exhibit impressive capabilities in generating realistic text across diverse subjects. Concerns have been raised that they could be utilized to produce fake content with a deceptive intention, although evidence thus far remains anecdotal. This paper presents a case study about a Twitter botnet that appears to employ ChatGPT to generate human-like content. Through heuristics, we identify 1,140 accounts and validate them via manual annotation. These accounts form a dense cluster of fake personas that exhibit similar behaviors, including posting machine-generated content and stolen images, and engage with each other through replies and retweets. ChatGPT-generated content promotes suspicious websites and spreads harmful comments. While the accounts in the AI botnet can be detected through their coordination patterns, current state-of-the-art LLM content classifiers fail to discriminate between them and human accounts in the wild. These findings highlight the threats posed by AI-enabled social bots.