Warfare has traditionally been considered unique to humans. It has, therefore, often been explained as deriving from features that are unique to humans, such as the possession of weapons or the adoption of a patriarchal ideology. Mounting evidence suggests, however, that coalitional killing of adults in neighboring groups also occurs regularly in other species, including wolves and chimpanzees. This implies that selection can favor components of intergroup aggression important to human warfare, including lethal raiding. Here I present the principal adaptive hypothesis for explaining the species distribution of intergroup coalitional killing. This is the “imbalance-of-power hypothesis,” which suggests that coalitional killing is the expression of a drive for dominance over neighbors. Two conditions are proposed to be both necessary and sufficient to account for coalitional killing of neighbors: (1) a state of intergroup hostility; (2) sufficient imbalances of power between parties that one party can attack the other with impunity. Under these conditions, it is suggested, selection favors the tendency to hunt and kill rivals when the costs are sufficiently low. The imbalance-of-power hypothesis has been criticized on a variety of empirical and theoretical grounds which are discussed. To be further tested, studies of the proximate determinants of aggression are needed. However, current evidence supports the hypothesis that selection has favored a hunt-and-kill propensity in chimpanzees and humans, and that coalitional killing has a long history in the evolution of both species. Yrbk Phys Anthropol 42:1–30, 1999. © 1999 Wiley-Liss, Inc.