Whole-chromosome copy number alterations, also known as aneuploidy, are associated with adverse consequences in most cells and organisms. However, high frequencies of aneuploidy have been reported to occur naturally in the mammalian liver and brain, fueling speculation that aneuploidy provides a selective advantage in these organs. To explore this paradox, we used single cell sequencing to obtain a genome-wide, high-resolution assessment of chromosome copy number alterations in mouse and human tissues. We find that aneuploidy occurs much less frequently in the liver and brain than previously reported and is no more prevalent in these tissues than in skin. Our results highlight the rarity of chromosome copy number alterations across mammalian tissues and argue against a positive role for aneuploidy in organ function. Cancer is therefore the only known example, in mammals, of altering karyotype for functional adaptation.