This article reexamines the conjecture of James S. Coleman that intergenerational social closure promotes student achievement in high schools, analyzing the best national data on academic achievement and social networks: the 2002 and 2004 waves of the Education Longitudinal Study. The results show that within the Catholic school sector, schools that are characterized by dense parental networks have substantially higher average student achievement. This association can be reduced but not eliminated by conditioning on available measures of student network structure and standard measures of family background. In contrast, in the public school sector, a similarly strong bivariate association between dense parental networks and student achievement can be attributed almost entirely to these basic conditioning variables. These results represent, at best, a mixed verdict for Coleman's predictions. Intergenerational closure in its currently observed form does not increase achievement in public schools, suggesting that parental monitoring of discipline does not outweigh some of the costs of parental closure. However, intergenerational closure may increase achievement in Catholic schools to a modest degree because Catholic schools are affiliated with religious communities that have appropriable norms. (Contains 2 figures, 4 tables and 11 notes.)