There is debate over whether Asian American students are admitted to selective colleges and universities at lower rates than white students with similar academic qualifications. However, there have been few empirical investigations of this issue, in large part due to a dearth of data. Here we present the results from analyzing 685,709 applications from Asian American and white students to a subset of selective U.S. institutions over five application cycles, beginning with the 2015-2016 cycle. The dataset does not include admissions decisions, and so we construct a proxy based in part on enrollment choices. Based on this proxy, we estimate the odds that Asian American applicants were admitted to at least one of the schools we consider were 28% lower than the odds for white students with similar test scores, grade-point averages, and extracurricular activities. The gap was particularly pronounced for students of South Asian descent (49% lower odds). We trace this pattern in part to two factors. First, many selective colleges openly give preference to the children of alumni, and we find that white applicants were substantially more likely to have such legacy status than Asian applicants, especially South Asian applicants. Second, after adjusting for observed student characteristics, the institutions we consider appear less likely to admit students from geographic regions with relatively high shares of applicants who are Asian. We hope these results inform ongoing discussions on the equity of college admissions policies.