Human adults often show a preference for scarce over abundant goods. In this paper, we investigate whether this preference was shared by 4- and 6-year-old children as well as chimpanzees, humans’ nearest primate relative. Neither chimpanzees nor 4-year-olds displayed a scarcity preference, but 6-year-olds did, especially in the presence of competitors. We conclude that scarcity preference is a human-unique preference that develops as humans increase their cognitive skills and social experiences with peers and competitors. We explore different potential psychological explanations for scarcity preference and conclude scarcity preference is based on children's fear of missing out an opportunity, especially when dealing with uncertainty or goods of unknown value in the presence of competitors. Furthermore, the results are in line with studies showing that supply-based scarcity increases the desirability of hedonic goods, suggesting that even as early as 6 years of age humans may use scarce goods to feel unique or special.