During genome replication, parental histones are recycled to newly replicated DNA with their posttranslational modifications (PTMs). It remains unknown whether sister chromatids inherit modified histones evenly. Here, we measured histone PTM partition to sister chromatids in embryonic stem cells. We found that parental histones H3-H4 segregate to both daughter DNA strands with a weak leading strand bias, skewing partition at topologically associating domain (TAD) borders and enhancers proximal to replication initiation zones. Segregation of parental histones to the leading strand increased markedly in cells with histone-binding mutations in MCM2, part of the replicative helicase, exacerbating histone PTM sister chromatid asymmetry. This work reveals how histones are inherited to sister chromatids and identifies a mechanism for how symmetric cell division is ensured by the replication machinery.