This paper explores the gains to monetary union. We consider a two-country overlapping generations model. Agents work when young and have random tastes over the composition (domestic vs. foreign goods) of old age consumption. In equilibrium, governments require that local currency be used for transactions as a means of creating a base for seignorage. Thus agents hold multiple currencies to deal with uncertainty in their optimal consumption bundles. We argue that this equilibrium is Pareto dominated by a monetary union, in which there is a single currency and a strong central bank that optimally chooses zero inflation. As suggested by the European Commissions' 1990 report, monetary union reduces the inefficiencies created by multiple currencies and leads to price stability. Finally, we argue this Pareto superior outcome can not be achieved without cooperation of the two governments.