ChatGPT sets a new record with the fastest-growing user base, as a chatbot powered by a large language model (LLM). While it demonstrates state-of-the-art capabilities in a variety of language-generating tasks, it also raises widespread public concerns regarding its societal impact. In this paper, we utilize natural language processing approaches to investigate the public attitudes towards ChatGPT by applying sentiment analysis and topic modeling techniques to Twitter data. Our result shows that the overall sentiment is largely neutral to positive, which also holds true across different occupation groups. Among a wide range of topics mentioned in tweets, the most popular topics are Artificial Intelligence, Search Engines, Education, Writing, and Question Answering.