Chromatin assembly mutants accumulate recombinogenic DNA damage and are sensitive to genotoxic agents. Here we have analyzed why impairment of the H3K56 acetylation-dependent CAF1 and Rtt106 chromatin assembly pathways, which have redundant roles in H3/H4 deposition during DNA replication, leads to genetic instability. We show that the absence of H3K56 acetylation or the simultaneous knock out of CAF1 and Rtt106 increases homologous recombination by affecting the integrity of advancing replication forks, while they have a minor effect on stalled replication fork stability in response to the replication inhibitor hydroxyurea. This defect in replication fork integrity is not due to defective checkpoints. In contrast, H3K56 acetylation protects against replicative DNA damaging agents by DNA repair/tolerance mechanisms that do not require CAF1/Rtt106 and are likely subsequent to the process of replication-coupled nucleosome deposition. We propose that the tight connection between DNA synthesis and histone deposition during DNA replication mediated by H3K56ac/CAF1/Rtt106 provides a mechanism for the stabilization of advancing replication forks and the maintenance of genome integrity, while H3K56 acetylation has an additional, CAF1/Rtt106-independent function in the response to replicative DNA damage.