I develop and estimate a structural equilibrium model of the college market. Students, having heterogeneous abilities and preferences, make college application decisions, subject to uncertainty and application costs. Colleges, observing only noisy measures of student ability, choose tuition and admissions policies to compete for more able students. Tuition, applications, admissions and enrollment are joint outcomes from a subgame perfect Nash equilibrium. I estimate the structural parameters of the model using data from the National Longitudinal Survey of Youth 1997, via a three-step procedure to deal with potential multiple equilibria. In counterfactual experiments, I use the model first to examine the extent to which college enrollment can be increased by expanding the supply of colleges, and then to assess the importance of various measures of student ability.