A country entering a monetary union gives up the right to determine its own monetary policy, thereby relinquishing monetary instruments to assure fiscal solvency. In this paper, we develop a new theoretical model to address fiscal solvency risk. We show that when debt is subject to an upper bound and policy faces stochastic shocks, a government can find itself in a position for which the expected present value of future surpluses under current policy is less than debt. Agents refuse to lend into such a position, and the sudden stop of capital flows defines a fiscal solvency crisis. We model the dynamics of a fiscal solvency crisis in a monetary union under the assumption that the fiscal authority will respond to the crisis using default to reduce the value of debt. We simulate the model to estimate fiscal solvency risk in the European Monetary Union. We find that countries adhering to the Stability and Growth Pack limits are perfectly safe, while countries like Greece and Italy, whose debt relative to GDP has strayed far above the 60 percent limit, are not.