The observation of karyotypic uniformity in most species has led to the widespread belief that selection limits chromosomal change. We report an unprecedented amount of chromosomal variation in a natural population of the South American marsh rat Holochilus brasiliensis. This variation consists of four distinct classes of chromosomal rearrangements: whole-arm translocations, pericentric inversions, variation in the amount of euchromatin, and variation in number and kind of supernumerary (B) chromosomes. Twenty-six karyotypes are present among 42 animals. Observations of the natural population over a 7-year period and breeding experiments with captive animals indicate that heterozygous individuals suffer no detectable reduction in fitness. This is at odds with a central assumption in current models of chromosomal speciation and provides a firm rejection of the view that selection necessarily restricts chromosomal change.