The histone chaperone Asf1 and the chromatin remodeler SWI/SNF have been separately implicated in derepression of the DNA damage response (DDR) genes in yeast cells treated with genotoxins that cause replication interference. Using genetic and biochemical approaches, we have tested if derepression of the DDR genes in budding yeast involves functional interplay between Asf1 and SWI/SNF. We find that Asf1 and SWI/SNF are both recruited to DDR genes under replication stress triggered by hydroxyurea, and have detected a soluble complex that contains Asf1 and the Snf2 subunit of SWI/SNF. SWI/SNF recruitment to DDR genes however does not require Asf1, and deletion of Snf2 does not affect Asf1 occupancy of DDR gene promoters. A checkpoint engagement defect is sufficient to explain the synthetic effect of deletion of ASF1 and SNF2 on derepression of the DDR genes in hydroxyurea-treated cells. Collectively, our results show that the DDR genes fall into a class in which Asf1 and SWI/SNF independently control transcriptional induction.