Differences in teacher quality are commonly cited as a key determinant of the huge international student performance gaps. However, convincing evidence on this relationship is still lacking, in part because it is unclear how to measure teacher quality consistently across countries. We use unique international assessment data to investigate the role of teacher cognitive skills as one main dimension of teacher quality in explaining student outcomes. Our main identification strategy exploits exogenous variation in teacher cognitive skills attributable to international differences in relative wages of nonteacher public sector employees. Using student-level test score data, we find that teacher cognitive skills are an important determinant of international differences in student performance. Results are supported by fixed-effects estimation that uses within-country between-subject variation in teacher skills.