While the goals of the integration of schools legally mandated by "Brown v. Board of Education" are very broad, here we focus more narrowly on how school racial composition affects scholastic achievement. Uncovering this effect is difficult, because racial mixing in the schools is not an accident but rather an outcome of both government and family choices. Our evaluation, made possible by rich panel data on the achievement of Texas students, disentangles racial composition effects from other aspects of school quality and from differences in abilities and family background. The results show that a higher percentage of black schoolmates has a strong adverse effect on the achievement of blacks and, moreover, that the effects are highly concentrated in the upper half of the skill distribution. In contrast, racial composition has a noticeably smaller effect on achievement of blacks with lower initial achievement and of whites--strongly suggesting that the results are not a simple reflection of unmeasured school quality. The uneven distribution of blacks across school districts can explain a significant portion of the black-white achievement gap in Texas. [Discussion Paper also supported by the Packard Humanities Institute.]