The packaging of the eukaryotic genome into chromatin is likely to be important for the maintenance of genomic integrity. Chromatin structures are assembled onto newly synthesized DNA by the action of chromatin assembly factors, including anti-silencing function 1 (ASF1). To investigate the role of chromatin structure in the maintenance of genomic integrity, we examined budding yeast lacking the histone chaperone Asf1p. We found that yeast lacking Asf1p accumulate in metaphase of the cell cycle due to activation of the DNA damage checkpoint. Furthermore, yeast lacking Asf1p are highly sensitive to mutations in DNA polymerase alpha and to DNA replicational stresses. Although yeast lacking Asf1p do complete DNA replication, they have greatly elevated rates of DNA damage occurring during DNA replication, as indicated by spontaneous Ddc2p-green fluorescent protein foci. The presence of elevated levels of spontaneous DNA damage in asf1 mutants is due to increased DNA damage, rather than the failure to repair double-strand DNA breaks, because asf1 mutants are fully functional for double-strand DNA repair. Our data indicate that the altered chromatin structure in asf1 mutants leads to elevated rates of spontaneous recombination, mutation, and DNA damage foci formation arising during DNA replication, which in turn activates cell cycle checkpoints that respond to DNA damage.