Cancer is principally considered a genetic disease, and numerous mutations are thought essential to drive its growth. However, the existence of genomically stable cancers and the emergence of mutations in genes that encode chromatin remodelers raise the possibility that perturbation of chromatin structure and epigenetic regulation are capable of driving cancer formation. Here we sequenced the exomes of 35 rhabdoid tumors, highly aggressive cancers of early childhood characterized by biallelic loss of SMARCB1, a subunit of the SWI/SNF chromatin remodeling complex. We identified an extremely low rate of mutation, with loss of SMARCB1 being essentially the sole recurrent event. Indeed, in 2 of the cancers there were no other identified mutations. Our results demonstrate that high mutation rates are dispensable for the genesis of cancers driven by mutation of a chromatin remodeling complex. Consequently, cancer can be a remarkably genetically simple disease.