Property as a social "agreement" comprises both a communicative component, in which someone makes a claim that she is entitled to some piece of property, and a cooperative component, in which others in the community respect that claim as legitimate. In the current study, preschool children were (a) given the opportunity to mark some objects as "theirs" (to claim them in the face of other fictitious children who would supposedly enter the room later); and (b) confronted with stickers in various spatial arrangements (e.g., piled up neatly vs. scattered), told that a fictitious child had previously chosen some for herself but had to suddenly leave the room, and then invited first to choose some stickers for themselves and second to identify which stickers had already been claimed by the fictitious child. Five-year-olds but not 3-year-olds were skillful in both of these tasks, demonstrating an understanding of the crucial role of communication in asserting property claims and the crucial role of cooperation in respecting them.