Lsm1 forms part of a cytoplasmic protein complex, Lsm1-7-Pat1, involved in the degradation of mRNAs. Here, we show that Lsm1 has an important role in promoting genomic stability in Saccharomyces cerevisiae. Budding yeast cells lacking Lsm1 are defective in recovery from replication-fork stalling and show DNA damage sensitivity. Here, we identify histone mRNAs as substrates of the Lsm1-7-Pat1 complex in yeast, and show that abnormally high amounts of histones accumulate in lsm1Δ mutant cells. Importantly, we show that the excess of histones is responsible for the lsm1Δ replication-fork instability phenotype, since sensitivity of lsm1Δ cells to drugs that stall replication forks is significantly suppressed by a reduction in histone gene dosage. Our results demonstrate that improper histone stoichiometry leads to genomic instability and highlight the importance of regulating histone mRNA decay in the tight control of histone levels in yeast.