Since the creation of the euro, capital flows among member countries have been large and volatile. Motivated by this fact, I provide a theory connecting the exchange rate regime to financial integration. The key feature of the model is that monetary policy affects the value of collateral that creditors seize upon default. Under flexible exchange rates, national governments can expropriate foreign creditors by depreciating the exchange rate, which induces investors to impose tight constraints on international borrowing. Creating a monetary union, by eliminating this source of currency risk, increases financial integration among member countries. This process, however, does not necessarily lead to higher welfare. The reason is that a high degree of capital mobility can generate multiple equilibria, with bad equilibria characterized by inefficient capital flights. Capital controls or fiscal transfers can eliminate bad equilibria, but their implementation requires international cooperation.