Asf1 is a conserved histone H3/H4 chaperone. We find that Asf1 in budding yeast promotes an essential cellular response to replication stress caused by the ribonucleotide reductase inhibitor hydroxyurea. That is, Asf1 stimulates derepression of DNA damage response (DDR) genes during the S phase. Derepression of DDR genes strongly correlates with Asf1 binding to their promoters. Having identified the C terminus and histone-binding domains of Asf1 as molecular determinants of its constitutive and inducible association with chromatin, we tested whether Asf1 binding to DDR genes is mechanistically important for their derepression. Our results provide little support for this hypothesis. Rather, the contribution of Asf1 to DDR gene derepression depends on its ability to stimulate H3K56 acetylation by lysine acetyltransferase Rtt109. The precise regulation of H3K56 acetylation in the promoters of DDR genes is unexpected: DDR gene promoters are occupied by H3K56-acetylated nucleosomes under repressing conditions, and the steady state level of H3K56 promoter acetylation does not change upon derepression. We propose that replication-coupled deposition of Lys(56)-acetylated H3 poises the DDR genes in newly synthesized daughter duplexes for derepression during the S phase. In this model, the presence of a histone mark that destabilizes nucleosomes is compatible with suppression of transcription because in the uninduced state, DDR gene promoters are constitutively occupied by a potent repressor-corepressor complex.