The inheritance of parental histones across the replication fork is thought to mediate epigenetic memory. Here, we reveal that fission yeast Mrc1 (CLASPIN in humans) binds H3-H4 tetramers and operates as a central coordinator of symmetric parental histone inheritance. Mrc1 mutants in a key connector domain disrupted segregation of parental histones to the lagging strand comparable to Mcm2 histone-binding mutants. Both mutants showed clonal and asymmetric loss of H3K9me-mediated gene silencing. AlphaFold predicted co-chaperoning of H3-H4 tetramers by Mrc1 and Mcm2, with the Mrc1 connector domain bridging histone and Mcm2 binding. Biochemical and functional analysis validated this model and revealed a duality in Mrc1 function: disabling histone binding in the connector domain disrupted lagging-strand recycling while another histone-binding mutation impaired leading strand recycling. We propose that Mrc1 toggles histones between the lagging and leading strand recycling pathways, in part by intra-replisome co-chaperoning, to ensure epigenetic transmission to both daughter cells.