This paper studies a social planner who chooses countries' carbon prices so as to maximize global welfare. Product markets are characterized by firm heterogeneity, market power, and international trade. Because of the market-power distortion, the planner's optimal policy is second-best. The main insight is that optimal carbon prices may be highly asymmetric: zero in some countries and above the social cost of carbon in countries with relatively dirty production. This result obtains even though a uniform global carbon price is always successful at reducing countries' emissions. Competition policy that mitigates market power may enable stronger and more balanced climate action.