We appeal to critical race theory and intersectionality to examine achievement gaps at a large public university in the American southwest from 2000 to 2015. Using white, high-income women as our reference group, we report linear combinations of marginal effects for six-year graduation rates and developmental course taking across 20 distinct social locations varying according to race-ethnicity, gender, and class. We find substantial achievement gaps that remain unseen in conventional models treating such characteristics as independent. Nearly every group has a significantly lower likelihood of graduation compared to the reference group, and there is substantial variation in estimated achievement gaps. Low-income, American Indian men are approximately 45 percent less likely to graduate within six years relative to the reference group. For high income, black men this gap is approximately 30 percent. Our paper proposes a method and praxis for exploring the complex, interdependent relationship between race-ethnicity, gender, and class.