Nuclear fission is capable of meeting global needs for carbon-free energy for millennia. However, the siting and implementation of waste repositories for spent fuel is becoming increasingly problematic from a financial and political perspective. We have performed initial studies of a novel concept for the permanent disposal of longlived fission waste, where "permanent" is defined as being on the billion-year time scale. The concept employs the heat from a compact, high-power-density fission reactor to melt a self-sealing channel, tens of kilometers down into the continental lithosphere. Partitioned long-lived fission waste is packaged at the rear of the device that melts its way through the rock at a descent rate set by the achievable reactor power density. The waste would be irretrievable and cannot return to the biosphere. Monitoring and longterm integrity of waste containers would not be required and disposal costs should be <1% of the cost-of-electricity. Design concepts for the reactor and the principle of molten rock boring are based on existing experimental and operational data.