In this paper we analyze the role played by self-confidence, modeled as beliefs about one's ability, in shaping task choices. We propose a model in which fully rational agents exploit all the available information to update their beliefs using Bayes' rule, eventually learning their true type. We show that when the learning process does not converge quickly to the true ability level, small differences in initial confidence can result in diverging patterns of human capital accumulation between otherwise identical individuals. If differences in self-confidence are correlated with socio-economic background (as a large body of empirical literature suggests), self-confidence can be a channel through which education and earning inequalities perpetuate across generations. Our theory suggests that cognitive tests should take place as early as possible, in order to avoid that systematic differences in self-confidence among equally talented people lead to the emergence of gaps in the accumulation of human capital. (Contains 1 table and 4 figures.)