Historically, commodity money preceded fiat money. Standard search-theoretical models of money such as Kiyotaki and Wright (1989) cannot explain this transition because of multiple equilibria: a small infusion of fiat money with superior intrinsic characteristics into a commodity money equilibrium is always valued if agents believe in its acceptability. We propose a natural extension of the standard model in order to break this indeterminacy. We assume (1) that agents derive positive utility from consuming even non-favorite commodities and (2) that agents have to consume regularly. We find that agents accept only commodity money if search frictions are large. Fiat money can become valuable in sufficiently advanced economies with small search frictions.