We consider a global externality of resource use, with the example of greenhouse gas emissions from fossil fuels. A region concerned about climate change may reduce its fuel deposit offer, reduce fuel consumption, and withdraw investments into global fuel extraction. We study leakage rates and optimal taxes on these three activities in a framework with uncertain fuel market returns. Without uncertainty, the unilateral investment tax is welfare-neutral: costless but ineffective divestment. With uncertainty, the regional investment choice affects global fuel usage, and correspondingly the optimal regional fuel policy contains a investment tax in addition to taxes on deposit supply and consumption. Even absent terms-of-trade effects, the optimal unilateral investment tax is a non-marginal fraction of the perceived climate disutility for a region of any size. Equivalently, a rational portfolio optimizer with relevant concern for the climate problem withdraws parts or all of her funds from the carbon sector.