The paper derives the global welfare-optimizing time path for a tax on fossil fuels causing a negative stock externality (climate change), under increasing marginal extraction cost, and in the presence of an unlimited backstop resource causing no externality. In a basic competitive case, the optimal tax equals the Pigou rate, equivalent to the present discounted value of marginal damage costs. We consider two separate types of tenure insecurity for resource owners, and their impact on the tax implementing the optimal policy. When insecure control is with respect to future ownership to the resource, competitive extraction is higher than otherwise, and the efficiency-implementing tax exceeds the Pigou rate. When tenure insecurity instead implies possible expropriation ("holdup") of investment in extraction capacity, it deters extraction, and the optimal tax is lower than the Pigou rate.