This research examines how school choice impacts school segregation. Specifically, this work demonstrates that even if parents do not take the racial demographics of schools into account, preference differences between Black and White parents for other school attributes can still result in segregation. These preference differences stem from motivational differences in pursuit of social status. Given that the de facto US racial hierarchy assigns Black people to a lower social status, Black parents are more motivated to seek schools that signal that they can improve their children's status. Simulations of parental school decisions at scale show that preference differences under an unmitigated school-choice policy lead to more segregated schools, impacting more than half a million US children for every 3-percentage-point increase in school-choice availability. In contrast, if Black and White parents have similar preferences, unmitigated school choice would reduce racial segregation. This research may inform public policy concerning school choice and school segregation.