We derive the optimal unilateral policy in a general equilibrium model of trade and climate change where one region of the world imposes a climate policy and the rest of the world does not. A climate policy in one region shifts activities—extraction, production, and consumption—in the other region. The optimal policy trades off the costs of these distortions. The optimal policy can be implemented through: (i) a nominal tax on extraction at a rate equal to the global marginal harm from emissions, (ii) a tax on imports of energy and goods, and a rebate of taxes on exports of energy but not goods, both at a lower rate than the extraction tax rate, and (iii) a goods-specific export subsidy. The policy controls leakage by combining supply-side and demand-side taxes to control the price of energy in the non-taxing region. It exploits international trade to expand the reach of the climate policy. We calibrate and simulate the model to illustrate how the optimal policy compares to more traditional policies such as extraction, production, and consumption taxes and combinations of those taxes. The simulations show that combinations of supply-side and demand-side taxes are much better than simpler policies and can perform nearly as well as the optimal policy.