I propose a new scenario for the discovery of America. By analogy with other successful animal invasions, one may assume that the discovery of the New World triggered a human population explosion. The invading hunters attained their highest population density along a front that swept from Canada to the Gulf of Mexico in 350 years, and on to the tip of South America in roughly 1000 years. A sharp drop in human population soon followed as major prey animals declined to extinction. Possible values for the model include an average frontal depth of 160 kilometers, an average population density of 0.4 person per square kilometer on the front and of 0.04 person per square kilometer behind the front, and an average rate of frontal advance of 16 kilometers per year. For the first two centuries the maximum rate of growth may have equaled the historic maximum of 3.4 percent annually. During the episode of faunal extinctions, the population of North America need not have exceeded 600,000 people at any one time. The model generates a population sufficiently large to overkill a biomass of Pleistocene large animals averaging 9 metric tons per square kilometer (50 animal units per section) or 2.3 x 10(8) metric tons in the hemisphere. It requires that on the front one person in four destroy one animal unit (450 kilograms) per week, or 26 percent of the biomass of an average section in 1 year in any one region. Extinction would occur within a decade. There was insufficient time for the fauna to learn defensive behaviors, or for more than a few kill sites to be buried and preserved for the archeologist. Should the model survive future findings, it will mean that the extinction chronology of the Pleistocene megafauna can be used to map the spread of Homo sapiens throughout the New World.