The gigantic volumes of carbon dioxide (CO2) removal likely needed to comply with the Paris Agreement beg the question of who should pay for the negative emissions. Incentivizing negative emissions is difficult, as it entails reversing the fiscal attractiveness associated with carbon taxes and emissions trading in favour of the more unattractive need to pay for removals. The inherent difficulty of funding global public goods associated with large private costs will make it hard for future governments to share this burden among themselves. We propose that this problem can be solved by a CO2 emitter liability operationalized through Atmospheric CO2 Removal Deposits (ACORDs). Anyone that emits fossil CO2 to the atmosphere would be obliged to finance the removal of at least as much CO2 from the atmosphere. Linking the liability to ACORDs acknowledges that a major part of the negative emissions needs to be made in the future. The emitters' financial deposits, including earnings, can be redeemed upon certified proof of removal. The ACORDs system would comply with the widely accepted principle of producer liability, i.e., that companies are responsible for the damage caused by their products. The system would also provide additional incentives to reduce emissions and an innovative funding source for coming generations to accomplish negative emissions. Furthermore, inequity and historical emissions can be addressed by gradually increasing overcompensation. The paper also includes a critical assessment of the basis of negative emissions, i.e., the need, the technologies and their potentials, the costs, and the required retention time.