We observe that a Pigovian climate policy need not exact full payment of the social cost of carbon upon emission to yield optimal incentives. Following this insight, we propose 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. This yields first-best emissions patterns. Because liabilities could be traded like financial debt, it also decentralizes the choice a discount rate as well as beliefs about the severity of the climate problem. From an informational standpoint, implementation relies only on realized damage and on the well-documented emission history of countries, unlike a carbon tax or tradable permits scheme, which are based on a sum of discounted expected future marginal damage.