Chromatin replication is intricately intertwined with the recycling of parental histones to the newly duplicated DNA strands for faithful genetic and epigenetic inheritance. The transfer of parental histones occurs through two distinct pathways: leading strand deposition, mediated by the DNA polymerase ε subunits Dpb3/Dpb4, and lagging strand deposition, facilitated by the MCM helicase subunit Mcm2. However, the mechanism of the facilitation of Mcm2 transferring parental histones to the lagging strand while moving along the leading strand remains unclear. Here, we show that the deletion of Pol32, a nonessential subunit of major lagging-strand DNA polymerase δ, results in a predominant transfer of parental histone H3-H4 to the leading strand during replication. Biochemical analyses further demonstrate that Pol32 can bind histone H3-H4 both in vivo and in vitro. The interaction of Pol32 with parental histone H3-H4 is disrupted through the mutation of the histone H3-H4 binding domain within Mcm2. Our findings identify the DNA polymerase δ subunit Pol32 as a critical histone chaperone downstream of Mcm2, mediating the transfer of parental histones to the lagging strand during DNA replication.