While there is a consensus that attending preschool better prepares children for kindergarten, evidence on the factors that sustain the preschool boost into the early elementary years is still emerging. To add to this literature, we use lottery data from applicants to oversubscribed schools in Boston Public Schools (BPS) prekindergarten program to estimate variation in the effects of the program across school sites through the end of third grade. Student outcomes include children's kindergarten-through-second-grade retention, kindergarten-through-third-grade special education placement, and third-grade state English Language Arts and math test scores. We find statistically significant variation in effects in all student outcomes and we predict this variation with multiple proxies for early elementary school quality. We find that the academic proficiency of third-graders within the schools for which prekindergarten children competed is most strongly associated with prekindergarten program effects. Prekindergarten gains persisted if students applied to and won a seat in a higher-quality elementary school. Our findings appear to be driven by the schools themselves and not by student selection in higher-scoring schools, nor by the counterfactual. These findings imply that policymakers and practitioners interested in sustained gains may need to also invest in improving the quality of children's K-3 experience.