During DNA replication newly synthesized histones are incorporated into the chromatin of the replicating sister chromatids. In the yeast Saccharomyces cerevisiae new histone H3 molecules are acetylated at lysine 56. This modification is carefully regulated during the cell cycle, and any disruption of this process is a source of genomic instability. Here we show that the protein kinase Dun1 is necessary in order to maintain viability in the absence of the histone deacetylases Hst3 and Hst4, which remove the acetyl moiety from histone H3. This lethality is not due to the well-characterized role of Dun1 in upregulating dNTPs, but rather because Dun1 is needed in order to counteract the checkpoint kinase Rad53 (human CHK2) that represses the activity of late firing origins. Deletion of CTF18, encoding the large subunit of an alternative RFC-like complex (RLC), but not of components of the Elg1 or Rad24 RLCs, is enough to overcome the dependency of cells with hyper-acetylated histones on Dun1. We show that the detrimental function of Ctf18 depends on its interaction with the leading strand polymerase, Polε. Our results thus show that the main problem of cells with hyper-acetylated histones is the regulation of their temporal and replication programs, and uncover novel functions for the Dun1 protein kinase and the Ctf18 clamp loader.