What would it take for aviation to become climate-neutral by 2050? We develop and model a trajectory for aviation to reduce its CO2 emissions by 90% by 2050, down to a level where all residual emissions can be removed from the atmosphere without crowding out other sectors that also need negative emissions. To make emitters pay for the carbon removal, we propose and model a negative emissions fund for airlines (NEFA). We show that it can pay for the removal of all CO2 emitted by aviation from 2030 onwards, for a contribution to the fund of USD 200–250 per ton CO2 emitted. In our baseline simulation, USD 3.3 trillion is invested by the fund over 40 years in high-quality carbon removal projects designed for biodiversity and societal co-benefits. While we do propose a number of governance principles and concrete solutions, our main goal is to start a societal dialogue to ensure aviation becomes both responsible and broadly beneficial.