Human populations have undergone dramatic expansions in size, but other than the growth associated with agriculture, the dates and magnitudes of those expansions have never been resolved. Here, we introduce two new statistical tests for population expansion, which use variation at a number of unlinked genetic markers to study the demographic histories of natural populations. By analyzing genetic variation in various aboriginal populations from throughout the world, we show highly significant evidence for a major human population expansion in Africa, but no evidence of expansion outside of Africa. The inferred African expansion is estimated to have occurred between 49,000 and 640,000 years ago, certainly before the Neolithic expansions, and probably before the splitting of African and non-African populations. In showing a significant difference between African and non-African populations, our analysis supports the unique role of Africa in human evolutionary history, as has been suggested by most other genetic work. In addition, the missing signal in non-African populations may be the result of a population bottleneck associated with the emergence of these populations from Africa, as postulated in the "Out of Africa" model of modern human origins.