We study optimal fiscal policy to address climate change and inequality. We theoretically characterize optimal carbon and income taxes, and quantify them for the US economy with the climate model calibrated to DICE. In contrast to the representative-agent setting, we find that (i) tax distortions have a negligible effect on the optimal carbon tax; (ii) inequality only slightly reduces it; (iii) the revenue from carbon taxes is optimally split halfway between reducing tax distortions and increasing transfers. Unlike the double-dividend policy, optimal carbon taxation has progressive welfare effects and low-income households benefit even in the short run. ( with Albert Jan Hummel and Marcelo Pedroni)