Significance Triplet repeat expansions cause nearly 20 inherited neurological diseases. The molecular mechanism of expansions is of interest at two levels. First is the basic science of how triplet repeats expand, and the second is the therapeutic opportunity to treat expansion diseases. This study presents evidence that addresses both areas of interest. We show that the histone deacetylase HDAC3 acts directly on the DNA mismatch repair protein MutSβ to stimulate CAG•CTG repeat expansions. This basic science insight into the mechanism also provides an explanation for how HDAC3 inhibition in Huntington’s disease mice leads to suppression of triplet repeat expansions and could therefore be considered as a therapy for Huntington’s disease and potentially other CAG•CTG repeat expansion diseases.