Abstract Speciation is often accompanied by changes in chromosomal number or form even though such changes significantly reduce the fertility of hybrid intermediates. We have addressed this evolutionary paradox by expanding the principle that nonrandom segregation of chromosomes takes place whenever human or mouse females are heterozygous carriers of Robertsonian translocations, a common form of chromosome rearrangement in mammals. Our analysis of 1170 mammalian karyotypes provides strong evidence that karyotypic evolution is driven by nonrandom segregation during female meiosis. The pertinent variable in this form of meiotic drive is the presence of differing numbers of centromeres on paired homologous chromosomes. This situation is encountered in all heterozygous carriers of Robertsonian translocations. Whenever paired chromosomes have different numbers of centromeres, the inherent asymmetry of female meiosis and the polarity of the meiotic spindle dictate that the partner with the greater number of centromeres will attach preferentially to the pole that is most efficient at capturing centromeres. This mechanism explains how chromosomal variants become fixed in populations, as well as why closely related species often appear to have evolved by directional adjustment of the karyotype toward or away from a particular chromosome form. If differences in the ability of particular DNA sequences or chromosomal regions to function as centromeres are also considered, nonrandom segregation is likely to affect karyotype evolution across a very broad phylogenetic range.