Recent research finds that pay inequality stems both from from pay-setting and from workers’ individual characteristics. Yet, intergenerational mobility research remains focused on transmission of individual traits, and has failed to test how firms shape the inheritance of inequality. We study this question using three decades of Swedish population register data, and decompose the intergenerational earnings correlation into firm pay premiums and stable worker effects. One quarter of the intergenerational earnings correlation at midlife is explained by sorting between firms with unequal pay. Employer or industry inheritance account for a surprisingly small share of this firm-based earnings transmission. Instead, children from high-income backgrounds benefit from matching with high-paying firms irrespective of the sources of parents’ earnings advantage. Our analysis reveals how an imperfectly competitive labor market provides an opening for skill-based rewards in one generation to become class-based advantages in the next.