We propose a new theory of Optimum Currency Areas (OCAs) based on monetary sovereignty. We consider two economically integrated countries with separate currencies and monetary policies, but with exchange rate underreaction. We show that the two countries are then engaged in a strategic monetization game, which may generate excessive inflation in equilibrium. A monetary union between the two countries can eliminate this excess inflation cost, but also removes a nation's monetary sovereignty. By eliminating the option to monetize debt in times of exigency, a monetary union may give rise to costly debt defaults. Joining a monetary union therefore involves trading excess monetization costs for debt default costs. Allowing for fiscal transfers within the union and for the option of debt monetization in a generalized crisis are optimal features of a monetary union. Our model also provides a coherent analytical framework that helps shed light on the recent history of OCAs.