Although essential for epigenetic inheritance, the transfer of parental histone (H3-H4)2 tetramers that contain epigenetic modifications to replicating DNA strands is poorly understood. Here, we show that the Mcm2-Ctf4-Polα axis facilitates the transfer of parental (H3-H4)2 tetramers to lagging-strand DNA at replication forks. Mutating the conserved histone-binding domain of the Mcm2 subunit of the CMG (Cdc45-MCM-GINS) DNA helicase, which translocates along the leading-strand template, results in a marked enrichment of parental (H3-H4)2 on leading strand, due to the impairment of the transfer of parental (H3-H4)2 to lagging strands. Similar effects are observed in Ctf4 and Polα primase mutants that disrupt the connection of the CMG helicase to Polα that resides on lagging-strand template. Our results support a model whereby parental (H3-H4)2 complexes displaced from nucleosomes by DNA unwinding at replication forks are transferred by the CMG-Ctf4-Polα complex to lagging-strand DNA for nucleosome assembly at the original location.