Carcinogenesis and neoplastic progression are mediated by the accumulation of somatic mutations. Here we report that the local density of somatic mutations in cancer genomes is highly reduced specifically in accessible regulatory DNA defined by DNase I hypersensitive sites. This reduction is independent of any known factors influencing somatic mutation density and is observed in diverse cancer types, suggesting a general mechanism. By analyzing individual cancer genomes, we show that the reduced local mutation density within regulatory DNA is linked to intact global genome repair machinery, with nearly complete abrogation of the hypomutation phenomenon in individual cancers that possess mutations in components of the nucleotide excision repair system. Together, our results connect chromatin structure, gene regulation and cancer-associated somatic mutation.