This paper presents a dynamic model of the decision to pursue a college education in which students face uncertainty about their future income stream after graduation due to unobserved heterogeneity in their innate scholastic ability. After students matriculate and start taking exams, they reevaluate their expectations about succeeding in college and may find it optimal to drop out and join the workforce without completing an undergraduate degree. The model shows that, in accordance with the data, poorer students are less likely to graduate and are more apt to drop out earlier than are wealthier students. Our model generates these results without introducing credit constraints. Conditioning on measures of innate ability, in the data we find that poor students are at least 27 percent more likely to drop out of college and they do so sooner than wealthier students.