Stratification researchers have reported that the relationship between family background and socio-economic outcomes drops to near zero for individuals who have a baccalaureate degree, leading one scholar to conclude that “This … provides a new answer to the old question about overcoming disadvantaged origins. A college degree can do it.” We present contrary evidence from two nationally representative samples of college graduates: the Baccalaureate & Beyond Longitudinal Study of 1993 and 2008. There are substantial income differences between graduates from different family backgrounds that can be observed both four and 10 years after graduation. These class-related gaps persist after controlling for college selectivity, major, and academic performance. Further analyses also indicate that these disadvantages in the labor market can be partially explained by inequalities established within occupational niches. We develop the implications of this for theories about the educational dimensions of intergenerational mobility.