We study a dynamic stochastic general equilibrium model where agents are concerned about model uncertainty regarding climate change. An externality from greenhouse gas emissions adversely affects the economy’s capital stock. We assume that the mapping from climate change to damages is subject to uncertainty, and we adapt and use techniques from robust control theory in order to study efficiency and optimal policy. We obtain a sharp analytical solution for the implied environmental externality, and we characterize dynamic optimal taxation. A small increase in the concern about model uncertainty can cause a significant drop in optimal energy extraction. The optimal tax which restores the social optimal allocation is Pigouvian. Under more general assumptions, we develop a recursive method and solve the model computationally. We find that the introduction of uncertainty matters qualitatively and quantitatively. We study optimal output growth in the presence and in the absence of concerns about uncertainty and find that these can lead to substantially different conclusions.