In theory, monetary policies that target the price level, as opposed to the inflation rate, should be highly effective at stabilizing the economy and avoiding deflation in the presence of the zero lower bound on nominal interest rates. With such a policy, if the short-term interest rate is constrained at zero and the inflation rate declines below its trend, the public expects that policy will eventually engineer a period of above-trend inflation that restores the price level to its target level. Expectations of future monetary accommodation stimulate output and inflation today, mitigating the effects of the zero bound. The effectiveness of such a policy strategy depends crucially on the alignment of the public's and the central bank's expectations of future policy actions. In this paper, we consider an environment where private agents have imperfect knowledge of the economy and therefore continuously reestimate the forecasting model that they use to form expectations. We find that imperfect knowledge on the part of the public, especially regarding monetary policy, can undermine the effectiveness of price-level-targeting strategies that would work well if the public had complete knowledge. For low inflation targets, the zero lower bound can cause a dramatic deterioration in macroeconomic performance with severe recessions occurring with alarming frequency. However, effective communication of the policy strategy that reduces the public's confusion about the future course of monetary policy significantly reduces the stabilization costs associated with the zero bound. Finally, the combination of learning and the zero bound implies the need for a stronger policy response to movements in the price level than would otherwise be optimal and such a rule is effective at stabilizing both inflation and output in the presence of learning and the zero bound even with a low inflation target.