To study the effects of ability grouping on school competition, we develop a theoretical and computational model of tracking in public and private schools. We examine tracking's consequences for the allocation of students of differing abilities and income within and between public and private schools. Private schools tend to attract the most able and wealthiest students, and rarely track in equilibrium. Public sector schools can maximize attendance by tracking students. Public schools retain a greater proportion of higher-ability students by tracking, but lose more wealthy, lower-ability students to the private sector. Consequently, socioeconomic status is a predictor of track assignment in public schools. For the entire population, public-sector tracking has small aggregate effects on achievement and welfare, but results in significant redistribution from lower- to higher-ability students.