Recombination, together with mutation, gives rise to genetic variation in populations. Here we leverage the recent mixture of people of African and European ancestry in the Americas to build a genetic map measuring the probability of crossing over at each position in the genome, based on about 2.1 million crossovers in 30,000 unrelated African Americans. At intervals of more than three megabases it is nearly identical to a map built in Europeans. At finer scales it differs significantly, and we identify about 2,500 recombination hotspots that are active in people of West African ancestry but nearly inactive in Europeans. The probability of a crossover at these hotspots is almost fully controlled by the alleles an individual carries at PRDM9 (P value < 10(-245)). We identify a 17-base-pair DNA sequence motif that is enriched in these hotspots, and is an excellent match to the predicted binding target of PRDM9 alleles common in West Africans and rare in Europeans. Sites of this motif are predicted to be risk loci for disease-causing genomic rearrangements in individuals carrying these alleles. More generally, this map provides a resource for research in human genetic variation and evolution.