This paper presents a study of preschool-aged children’s knowledge of the semantics of the negative polarity item (NPI) any. NPIs like any differ in distribution from non-polarity-sensitive indefinites like a: any is restricted to downward-entailing linguistic environments (Fauconnier 1975, 1979; Ladusaw 1979). But any also differs from plain indefinites in its semantic contribution; any can quantify over wider domains of quantification than plain indefinites. In fact, on certain accounts of NPI licensing, it is precisely the semantics of any that derives its restricted distribution (Kadmon & Landman 1993; Krifka 1995; Chierchia 2006, 2013). While previous acquisition studies have investigated children’s knowledge of the distributional constraints on any (O’Leary & Crain 1994; Thornton 1995; Xiang, Conroy, Lidz & Zukowski 2006; Tieu 2010), no previous study has targeted children’s knowledge of the semantics of the NPI. To address this gap in the existing literature, we present an experiment conducted with English-speaking adults and 4–5-year-old children, in which we compare their interpretation of sentences containing any with their interpretation of sentences containing the plain indefinite a and the bare plural. When presented with multiple domain alternatives, one of which was made more salient than the others, both adults and children restricted the domain of quantification for the plain indefinites to the salient subdomain. In the case of any, however, the adults and most of the children that we tested interpreted any as quantifying over the largest domain in the context. We discuss our findings in light of theories of NPI licensing that posit a connection between the distribution of NPIs and their underlying semantics, and conclude by raising further questions about the learnability of NPIs.