Current knowledge about social behavior of free-ranging domestic dogs is scarce, and the possibility that they could form stable social groups has been highly debated. We investigated the existence of a social-dominance hierarchy in a free-ranging group of domestic dogs. We quantified the pattern of dyadic exchange of a number of behaviors to examine to what extent each behavior fits a linear rank-order model. We distinguished among agonistic dominance, formal dominance, and competitive ability. The agonistic-dominance hierarchy in the study group shows significant and substantial linearity. As in random assortments of captive wolves, there is a prominent but nonexclusive male agonistic dominance in each age class. The agonistic rank-order correlates positively and significantly with age. Submissive–affiliative behavior fulfills the criteria of formal submission signals; nevertheless, it was not observed among all dogs, and thus, it is not useful to order the dogs in a consistent linear rank. Agonistic-dominance relationships in the dog group remain stable across different competitive contexts and to the behaviors considered. Some individuals gain access to food prevailing over other dogs during competitions. Access to food resources is predicted reasonably well by agonistic rank order: High-ranking individuals have the priority of access. The findings of this research contradict the notion that free-ranging dogs are “asocial” animals and agree with other studies suggesting that long-term social bonds exist within free-ranging dog groups.