Inflation-targeting central banks have only imperfect knowledge about the effect of policy decisions on inflation. An important source of uncertainty is the relationship between inflation and unemployment. This paper studies the optimal monetary policy in the presence of uncertainty about the natural unemployment rate, the short-run inflation-unemployment tradeoff and the degree of inflation persistence in a simple macroeconomic model that incorporates rational learning by the central bank as well as market participants. Two conflicting motives drive the optimal policy. In the static version of the model, uncertainty provides a motive for the policymaker to move more cautiously than she would if she knew the true parameters. In the dynamic version, uncertainty also motivates an element of experimentation in policy. The optimal policy, which balances the cautionary and activist motives, is computed using empirical estimates of Phillips curve uncertainty. Experimentation matters quantitatively for moderate to high degrees of uncertainty. Nevertheless, gradual inflation stabilization typically remains optimal, that is, the optimal policy response to inflation is less aggressive than a policy that disregards parameter uncertainty. Exceptions occur when uncertainty is very high and inflation close to target.