Given the dramatic risks and rewards to different graduate pathways, it is imperative to understand disparities in access to the highest levels of education. This paper responds to a tension between the traditional understanding that parents' education ceases to influence children's educational trajectories after college and the more recent reemergence of family background as a predictor of children's socioeconomic attainment. This paper asks two questions: to what extent is parental educational background associated with (1) graduate enrollment overall and (2) enrollment into particular credentials (e.g. master's, professional, and research doctoral degrees)? Drawing on data from the 2008-18 Baccalaureate and Beyond study, findings reveal that parental educational background, especially parental graduate degrees, are associated with enrollment into graduate school. By using two measures of parental education and disaggregating the outcome into different credentials, this paper shows that highly educated parents are associated with a greater advantage for doctoral enrollment than for master's enrollment. Due to the close ties between doctoral credentials and elite, high-paying occupations, this study has implications for inequality in higher education and economic inequality more broadly. [This paper will be published in "The Journal of Higher Education."]