The rationale is disclosed for a substructure within the Earth's inner core, consisting of an actinide subcore at the center of the Earth, surrounded by a subshell composed of the products of nuclear fission and radioactive decay. Estimates are made as to possible densities, physical dimensions, and chemical compositions. The feasibility for self-sustaining nuclear fission within the subcore is demonstrated, and implications bearing on the structure and geodynamic activity of the inner core are discussed.