We argue for the creation of a carbon liabilities market to address climate change. Each period, countries would be made liable for their share of responsibility in current climate damage. Because liabilities could be traded like financial debt, robustness to strategic manipulations and efficiency ensue. Moreover, this decentralizes the choice of the rate by which countries discount future benefits and damage. Rather than being based on an expected discounted sum of future marginal damage (as with a carbon tax or tradable emission permits) our proposal relies only on observed realized damage and on the well-documented emission history of countries.