Break-induced replication (BIR) has been implicated in restoring eroded telomeres and collapsed replication forks via single-ended invasion and extensive DNA synthesis on the recipient chromosome. Unlike other recombination subtypes, DNA synthesis in BIR likely relies heavily on mechanisms enabling efficient fork progression such as chromatin modification. Herein we report that deletion of HST3 and HST4, two redundant de-acetylases of histone H3 Lysine 56 (H3K56), inhibits BIR, sensitizes checkpoint deficient cells to deoxyribonucleotide triphosphate pool depletion, and elevates translocation-type gross chromosomal rearrangements (GCR). The basis for deficiency in BIR and gene conversion with long gap synthesis in hst3Δ hst4Δ cells can be traced to a defect in extensive DNA synthesis. Distinct from other cellular defects associated with deletion of HST3 and HST4 including thermo-sensitivity and elevated spontaneous mutagenesis, the BIR defect in hst3Δ hst4Δ cannot be offset by the deletion of RAD17 or MMS22, but rather by the loss of RTT109 or ASF1, or in combination with the H3K56R mutation, which also restores tolerance to replication stress in mrc1 mutants. Our studies suggest that acetylation of H3K56 limits extensive repair synthesis and interferes with efficient fork progression in BIR.