This paper presents a continuous-time stochastic model to study the timing decision of strategic default of sovereign debt. The debtor country precommits to an investment plan, finances part of it with a foreign loan, and maximizes the present value (PV) of utility from an infinite stream of consumption. Default risk arises from uncertainty surrounding the evolution of GDP over time. As the debt ratio increases, it introduces an increasing drag on the growth of GDP and also increases the risk premium on the loans, At each moment the nation must decide whether to service the loan over the next period (infinitesimally small) or to default, thereby gaining the PV of the loan, but correspondingly suffering a default penalty, and forgoing the option to default in the future. This choice is cast as a first-passage problem: default occurs (if and) when the PV of consumption under default first exceeds the PV given continuance of debt service. The actual values of the debt ratio for several debt-ridden countries is found to be close to the theoretically derived critical level. This framework also enables the study of austerity programs, rescheduling and other policy alternatives.