I explore the welfare implications of currency union (CU) membership in a model that generates a trade-off between alternative monetary arrangements. While national currencies support country-specific monetary policies, a CU eliminates some barriers to trade and transitory cross-border price misalignments caused by nominal rigidities. I quantify the welfare gap between these two arrangements and show that it depends crucially on the correlation of shocks across the countries involved. I estimate the model with data from 11 Eurozone members and I seek the minimum trade gains needed to make a single currency worthwhile for them. I find that modest trade gains are likely to be sufficient, given the good business-cycle affiliation of these economies.