Carbon-14 radiotracer experiments at 10 kbar (1 GPa) and 1000¿-1200¿C reveal that, due to low diffusivity or low solubility (or both), carbon is immobile in the grain boundary regions of natural dunite. Within the resolution of the beta-track mapping technique, grain boundary diffusion of carbon from a pure graphite source is not detectable in experiments of up to 10 days duration at 1200¿C, even though measurable volume diffusion profiles are generated at these conditions (D~3-4¿10-10 cm2/s, in agreement with previous estimates). The documented immobility of carbon in dunite grain boundaries precludes development of a continuous carbon film by diffusion from an initially localized source. If such a film is the cause of the mantle high-conductivity layer, it probably originated by a process involving fluid (CO/CO2) infiltration and subsequent reduction.