The financial crisis and the subsequent world-wide recession has led to a ballooning of government debt. This paper examines the implications of high government debt for optimal monetary policy in response to a large recessionary shock in a Blanchard-Yaari economy. In the model, the required risk premium on government debt is a function of the debt to GDP ratio and conventional monetary policy is constrained by the lower bound on the riskless short-term interest rate. We find that under the optimal policy the central bank reduces the risk premium on government debt to stabilise the economy. In the process, it expands its balance sheet and needs to rely less on forward guidance.