After three decades of decline, the amount of time spent by parents on childcare in the U.S. began to rise dramatically in the mid-1990s. Moreover, the rise in childcare time was particularly pronounced among college-educated parents. Why would highly educated parents increase the amount of time they allocate to childcare at the same time that their own market returns have skyrocketed? After finding no empirical support for standard explanations, such as selection or income effects, we offer a new explanation. We argue that increased competition for college admissions may be an important source of these trends. The number of college-bound students has surged in recent years, coincident with the rise in time spent on childcare. The resulting "cohort crowding" has led parents to compete more aggressively for college slots by spending increasing amounts of time on college preparation. Our theoretical model shows that, since college-educated parents have a comparative advantage in college preparation, rivalry leads them to increase preparation time by a greater amount than less-educated parents. We provide empirical support for our explanation with a comparison of trends between the U.S. and Canada, and a comparison across racial groups in the U.S.