The recently released artificial intelligence conversational agent, ChatGPT, has gained significant attention in academia and real life. A multitude of early ChatGPT users eagerly explore its capabilities and share their opinions on it via social media. Both user queries and social media posts express public concerns regarding this advanced dialogue system. To mine public concerns about ChatGPT, a novel Self-Supervised neural Topic Model (SSTM), which formalizes topic modeling as a representation learning procedure, is proposed in this paper. Extensive experiments have been conducted on Twitter posts about ChatGPT and queries asked by ChatGPT users. And experimental results demonstrate that the proposed approach could extract higher quality public concerns with improved interpretability and diversity, surpassing the performance of state-of-the-art approaches.