Many of the most virulent emerging infectious diseases in humans, e.g., AIDS and Ebola, are zoonotic, having shifted from wildlife populations. Critical questions for predicting disease emergence are: (1) what determines when and where a disease will first cross from one species to another, and (2) which factors facilitate emergence after a successful host shift. In wild primates, infectious diseases most often are shared between species that are closely related and inhabit the same geographic region. Therefore, humans may be most vulnerable to diseases from the great apes, which include chimpanzees and gorillas, because these species represent our closest relatives. Geographic overlap may provide the opportunity for cross-species transmission, but successful infection and establishment will be determined by the biology of both the host and pathogen. We extrapolate the evolutionary relationship between pathogen sharing and divergence time between primate species to generate "hotspot" maps, highlighting regions where the risk of disease transfer between wild primates and from wild primates to humans is greatest. We find that central Africa and Amazonia are hotspots for cross-species transmission events between wild primates, due to a high diversity of closely related primate species. Hotspots of host shifts to humans will be most likely in the forests of central and west Africa, where humans come into frequent contact with their wild primate relatives. These areas also are likely to sustain a novel epidemic due to their rapidly growing human populations, close proximity to apes, and population centers with high density and contact rates among individuals.