We develop a measure of maximum sustainable government debt for advanced economies. How much investors are willing to lend to a country's government depends on the country's expected primary surplus, the level and volatility of its rate of growth, and how much debt the government expects to be able to raise in the future for the purpose of servicing the debt it seeks to raise today. We provide a simple formula that computes a country's maximum sustainable debt (MSD) as a function of four easy-to-estimate parameters. We further compute a country's theoretical probability of default (PD) as a function of its debt-to-GDP ratio. We finally calibrate our measures for 23 OECD countries and test the relation between sovereign yield spreads and our theoretical PD at prevailing debt levels. We find it to be strongly statistically significant.