Solid-state conducting polymers usually have highly conjugated macromolecular backbones and require intentional doping in order to achieve high electrical conductivities. Conversely, single-component, charge-neutral macromolecules could be synthetically simpler and have improved processibility and ambient stability. We show that poly(4-glycidyloxy-2,2,6,6-tetramethylpiperidine-1-oxyl), a nonconjugated radical polymer with a subambient glass transition temperature, underwent rapid solid-state charge transfer reactions and had an electrical conductivity of up to 28 siemens per meter over channel lengths up to 0.6 micrometers. The charge transport through the radical polymer film was enabled with thermal annealing at 80 degrees C, which allowed for the formation of a percolating network of open-shell sites in electronic communication with one another. The electrical conductivity was not enhanced by intentional doping, and thin films of this material showed high optical transparency.