We study a dynamic stochastic general equilibrium model in which agents are concerned about model uncertainty regarding climate change. An externality from greenhouse gas emissions damages the economy's capital stock. We assume that the mapping from climate change to damages is subject to uncertainty, as opposed to risk, and we use robust control to study efficiency and optimal policy. We obtain a sharp analytical solution for the implied environmental externality and characterize dynamic optimal taxation. The optimal tax that restores the socially optimal allocation is Pigouvian. We study optimal output growth in the presence and in the absence of concerns about model uncertainty, and find that these can lead to substantially different conclusions regarding the optimal emissions and the optimal mix of fossil fuel. In particular, the optimal use of coal will be significantly lower on a robust path, while the optimal use of oil/gas will edge down.