In Saccharomyces cerevisiae, histone H3 lysine 56 acetylation (H3K56ac) occurs in newly synthesized histones that are deposited throughout the genome during DNA replication. Defects in H3K56ac sensitize cells to genotoxic agents, suggesting that this modification plays an important role in the DNA damage response. However, the links between histone acetylation, the nascent chromatin structure, and the DNA damage response are poorly understood. Here we report that cells devoid of H3K56ac are sensitive to DNA damage sustained during transient exposure to methyl methanesulfonate (MMS) or camptothecin but are only mildly affected by hydroxyurea. We demonstrate that, after exposure to MMS, H3K56ac-deficient cells cannot complete DNA replication and eventually segregate chromosomes with intranuclear foci containing the recombination protein Rad52. In addition, we provide evidence that these phenotypes are not due to defects in base excision repair, defects in DNA damage tolerance, or a lack of Rad51 loading at sites of DNA damage. Our results argue that the acute sensitivity of H3K56ac-deficient cells to MMS and camptothecin stems from a failure to complete the repair of specific types of DNA lesions by recombination and/or from defects in the completion of DNA replication.