Human DNA diversity arises ultimately from germline mutation that creates new haplotypes that can be reshuffled by meiotic recombination. Reciprocal crossover generates recombinant haplotypes but should not influence the frequencies of alleles in a population. We demonstrate crossover asymmetry at a recombination hot spot in the major histocompatibility complex, whereby reciprocal exchanges in sperm map to different locations in the hot spot. We identify a single-nucleotide polymorphism at the center of the hot spot and show that, when heterozygous, it seems sufficient to cause this asymmetry, apparently by influencing the efficiency of highly localized crossover initiation. As a consequence, crossovers in heterozygotes are accompanied by biased gene conversion, most likely occurring by gap repair, that can also affect nearby polymorphisms through repair of an extended gap. The result is substantial over-transmission of the recombination-suppressing allele and neighboring markers to crossover products. Computer simulations show that this meiotic drive, although weak at the population level, is sufficient to favor eventual fixation of the recombination-suppressing variant. These findings provide an explanation for the relatively uniform widths of human crossover hot spots and suggest that hot spots may be generally prone to extinction by meiotic drive.