Student gender differences in technology acceptance and use have persisted for years, giving rise to equity concerns in higher education (HE). To explore if such differences extend to generative artificial intelligence (genAI) chatbot use, we surveyed a large Norwegian HE student sample (n = 2692) using a fully mixed concurrent equal status design. Our findings show that men exhibit more frequent engagement with genAI chatbots across a broader spectrum of applications. Further, men demonstrate a heightened interest in genAI chatbots as tools and in their relevance to future career prospects. Women primarily utilize genAI chatbots in text-related tasks and express greater concerns regarding critical and independent thinking. Women also exhibit a stronger need to learn how to determine when it is wise to use and how to trust genAI chatbots. Consequences are discussed for the individual, society, and HE institutions in terms of social reproduction, diversity competence, and equitable teaching practices.