We develop a behavioral New Keynesian model to analyze optimal monetary policy with heterogeneously myopic households and firms. Five key results are derived. First, our model reflects coherent microeconomic and aggregate myopia due to the consistent transition from subjective to objective expectations. Second, the optimal monetary policy entails implementing inflation targeting in a framework where myopia distorts agents' inflation expectations. Third, price level targeting emerges as the optimal policy under output gap, revenue, or interest rate myopia. Given that bygones are not bygones under price level targeting, rational inflation expectations are a minimal condition for optimality under bounded rationality. Fourth, we show that there are no feasible instrument rules for implementing the optimal monetary policy, casting doubt on the ability of simple Taylor rules to assist in the setting of monetary policy when agents are myopic. Finally, bounded rationality is not necessarily welfare decreasing, and is even associated with welfare gains for extreme cognitive discounting.