Rising between-firm pay dispersion accounts for the majority of the dramatic increase in earnings inequality in the United States in the last several decades. This paper shows that a distinct cross-cohort pattern drives this rise: newer cohorts of firms enter more dispersed and stay more dispersed throughout their lives. These cohort patterns suggest a link between changes in firm entry associated with the decline in business dynamism and the rise in earnings inequality. Cohort effects also imply a slow diffusion of inequality: inequality rises as younger and more unequal cohorts of firms replace older and more equal cohorts.