The COVID-19 epidemic in emerging markets risks a combined health, economic, and debt crisis. We integrate a standard epidemiology model into a sovereign default model and study how default risk impacts the ability of these countries to respond to the epidemic. Lockdown policies are useful for alleviating the health crisis but they carry large economic costs and can generate costly and prolonged debt crises. The possibility of lockdown induced debt crises in turn results in less aggressive lockdowns and a more severe health crisis. We find that the social value of debt relief can be substantial because it can prevent the debt crisis and can save lives.