The histone variant H2A.Z plays key roles in gene expression, DNA repair, and centromere function. H2A.Z deposition is controlled by SWR-C chromatin remodeling enzymes that catalyze the nucleosomal exchange of canonical H2A with H2A.Z. Here we report that acetylation of histone H3 on lysine 56 (H3-K56Ac) alters the substrate specificity of SWR-C, leading to promiscuous dimer exchange in which either H2A.Z or H2A can be exchanged from nucleosomes. This result was confirmed in vivo, where genome-wide analysis demonstrated widespread decreases in H2A.Z levels in yeast mutants with hyperacetylated H3K56. Our work also suggests that a conserved SWR-C subunit may function as a "lock" that prevents removal of H2A.Z from nucleosomes. Our study identifies a histone modification that regulates a chromatin remodeling reaction and provides insights into how histone variants and nucleosome turnover can be controlled by chromatin regulators.