I investigate the importance of the match between teachers and schools for student achievement. I show that teacher effectiveness is higher after a move to a different school, and I estimate teacher-school match effects using a mixed effects estimator. Match quality can "explain away" a quarter of, and is as economically important as, teacher quality. Supporting models of worker mobility, teachers tend to exit schools with which match quality is low, and match quality is increasing in experience. This paper provides some of the first estimates of worker-firm match quality using output data as opposed to inferring productivity from wages or employment durations.