We envision the creation of a climate liability market to address climate change. Each period, countries are issued liability commensurate to their emissions of the period. Liability bearers are required to pay over time, as climate harm materializes. Revenues are used to compensate participating countries in proportion of climate harm. Because liabilities are traded like financial debt among participants, the mechanism achieves a unique carbon price through decentralization of the choice of a discount rate as well as beliefs about the severity of the climate problem. We discuss properties of such a mechanism along the dimensions of efficiency, fairness, exposure to risk, commitment, participation, as well as implementation challenges.