Inheritance of epigenetic information is critical for maintaining cell identity. The transfer of parental histone H3-H4 tetramers, the primary carrier of epigenetic modifications on histone proteins, represents a crucial yet poorly understood step in the inheritance of epigenetic information. Here, we show the lagging strand DNA polymerase, Pol δ, interacts directly with H3-H4 and that the interaction between Pol δ and the sliding clamp PCNA regulates parental histone transfer to lagging strands, most likely independent of their roles in DNA synthesis. When combined, mutations at Pol δ and Mcm2 that compromise parental histone transfer result in a greater reduction in nucleosome occupancy at nascent chromatin than mutations in either alone. Last, PCNA contributes to nucleosome positioning on nascent chromatin. On the basis of these results, we suggest that the PCNA-Pol δ complex couples lagging strand DNA synthesis to parental H3-H4 transfer, facilitating epigenetic inheritance.