Unlike gender or race, class background is rarely a focus of research on career progression, or of DEI efforts in elite occupations. Should it be? In this paper we document a large class gap in career progression in one occupation – US tenure-track academia – using parental education to proxy for class background. First-generation college graduates are 10% less likely to be tenured at an R1, are tenured at institutions ranked 11% lower, earn 3% less, and report 5% lower job satisfaction, than their former PhD classmates (from the same institution and field) with a parent with a non-PhD graduate degree. Neither selection out of academia nor different preferences explain this gap; differential research productivity also plays little role. Instead, likely drivers are differences in cultural and social capital. We also find a class gap in career progression for PhDs who work in industry, suggesting this phenomenon generalizes outside academia.