Countries around the world are adopting market-oriented school choice reforms. Evidence shows that they affect both student and teacher sorting across school sectors. Previous studies have analyzed student and teacher sorting in isolation from each other. This is the first paper to unify parental school choice and teacher sorting in an equilibrium framework. Using data from the large-scale Chilean voucher plan, this paper extends the existing literature in three ways. First, it evaluates how much of the treatment effect of Chilean voucher schools is due to teacher quality. Second, it examines the welfare implications of school specialization in different types of students. Third, it evaluates the impact of school choice expansion with endogenous public and private school teacher quality. There are three main results. First, better teacher quality accounts for 19 percent of the private school effectiveness in Chile. Second, assortative matching of students to teachers by ability can be welfare improving for low-ability students if the schools that have less able teachers are also those that specialize in the weakest students. Third, under the Chilean plan, highly skilled teachers are attracted into private schools from outside of teaching, with only limited cream skimming of teachers from public schools.