Genome instability is associated with tumorigenesis. Here, we identify a role for the histone Htz1, which is deposited by the Swr1 chromatin-remodeling complex (SWR-C), in preventing genome instability in the absence of the replication fork/replication checkpoint proteins Mrc1, Csm3, or Tof1. When combined with deletion of SWR1 or HTZ1, deletion of MRC1, CSM3, or TOF1 or a replication-defective mrc1 mutation causes synergistic increases in gross chromosomal rearrangement (GCR) rates, accumulation of a broad spectrum of GCRs, and hypersensitivity to replication stress. The double mutants have severe replication defects and accumulate aberrant replication intermediates. None of the individual mutations cause large increases in GCR rates; however, defects in MRC1, CSM3 or TOF1 cause activation of the DNA damage checkpoint and replication defects. We propose a model in which Htz1 deposition and retention in chromatin prevents transiently stalled replication forks that occur in mrc1, tof1, or csm3 mutants from being converted to DNA double-strand breaks that trigger genome instability.