We study optimal monetary policy at the zero lower bound. The macroeconomy we study has considerable income inequality which gives rise to a large private sector credit market. Households participating in this market use non-state contingent nominal contracts (NSCNC). A second, small group of households only uses cash and cannot participate in the credit market. The monetary authority supplies currency to cash-using households in a way that changes the price level to provide for optimal risk-sharing in the private credit market and thus to overcome the NSCNC friction. For sufficiently large and persistent negative shocks the zero lower bound on nominal interest rates may threaten to bind. The monetary authority may credibly promise to increase the price level in this situation to maintain a smoothly functioning (complete) credit market. The optimal monetary policy in this model can be broadly viewed as a version of nominal GDP targeting.