AI-powered chat technology is an emerging topic worldwide, particularly in areas such as education, research, writing, publishing, and authorship. This study aims to explore the factors driving students' acceptance of ChatGPT in higher education. The study employs the unified theory of acceptance and use of technology (UTAUT2) theoretical model, with an extension of Personal innovativeness, to verify the Behavioral intention and Use behavior of ChatGPT by students. The study uses data from a sample of 503 Polish state university students. The PLS-SEM method is utilized to test the model. Results indicate that Habit has the most significant impact (0.339) on Behavioral intention, followed by Performance expectancy (0.260), and Hedonic motivation (0.187). Behavioral intention has the most significant effect (0.424) on Use behavior, followed by Habit (0.255) and Facilitating conditions (0.188). The model explains 72.8% of the Behavioral intention and 54.7% of the Use behavior variance. While the study is limited by the sample size and selection, it is expected to be a starting point for more research on ChatGPT-like technology in university education, given that this is a recently introduced technology.