We determine optimal monetary policy under commitment in a forwardlooking New Keynesian model when nominal interest rates are bounded below by zero. The lower bound represents an occasionally binding constraint that causes the model and optimal policy to be nonlinear. A calibration to the U.S. economy suggests that policy should reduce nominal interest rates more aggressively than suggested by a model without lower bound. Rational agents anticipate the possibility of reaching the lower bound in the future and this amplifies the effects of adverse shocks well before the bound is reached. While the empirical magnitude of U.S. mark-up shocks seems too small to entail zero nominal interest rates, shocks affecting the natural real interest rate plausibly lead to a binding lower bound. Under optimal policy, however, this occurs quite infrequently and does not imply positive average inflation rates in equilibrium. Interestingly, the presence of binding real rate shocks alters the policy response to (non-binding) markup shocks.