A basic problem of daily life is determining who owns what. One way that people may solve this problem is by relying on a 'first possession' heuristic, according to which the first person who possesses an object is its owner, even if others subsequently possess the object. We investigated preschoolers' use of this heuristic in five experiments. In Experiments 1 and 2, 3- and 4-year-olds inferred that an object was owned by the character who possessed it first, even though another character subsequently possessed it. Two-year-olds also showed this bias, but only when the object was placed between the characters when children were asked about ownership. Experiment 3 ruled out the possibility that children's bias to select the first possessor results from a tendency to select the character first associated with the object. Experiment 4 showed that 3- and 4-year-olds have difficulty disregarding the first possession heuristic, even when provided with evidence that the character who first possessed an object is not its owner. But Experiment 5 found that children can disregard the heuristic in at least some situations. These five experiments suggest that the first possession heuristic guides children's ownership inferences. The findings provide the first evidence that preschoolers can infer who owns what, when not explicitly told, and when not reasoning about objects with which they are personally acquainted.