We study counterfeiting of currency in a search-theoretic model of monetary exchange. In contrast to Nosal and Wallace [Journal of Monetary Economics 54, 229–246 (2007)], we establish that counterfeiting does not pose a threat to the existence of a monetary equilibrium; i.e., a monetary equilibrium exists irrespective of the cost of producing counterfeits, or the ease with which genuine money can be authenticated. However, the possibility of counterfeiting fiat money can affect its value, velocity, output, and welfare, even if no counterfeiting occurs in equilibrium. We provide two extensions of the model under which the threat of counterfeiting can materialize: counterfeits can circulate across periods, and sellers set terms of trade in some matches. Policies that make the currency more costly to counterfeit or easier to recognize raise the value of money and society's welfare, but the latter policy does not always decrease counterfeiting.