Natural graphite was intercalated, thermally exfoliated, and dispersed in acetone to prepare graphite nanoplatelets (GNPs, G(n)) of controlled aspect ratio. Thermal conductivity measurements indicate that few graphene layer G(n), where n similar to 4, with a thickness of similar to 2 nm function as a very efficient filler for epoxy composites. When embedded in an epoxy matrix, the G(4) GNPs provide a thermal conductivity enhancement of more than 3000% (loading of similar to 25 vol %), and a thermal conductivity kappa = 6.44 W/mK, which surpasses the performance of conventional fillers that require a loading of similar to 70 vol % to achieve these values. We attribute the outstanding thermal properties of this material to a favorable combination of the high aspect ratio, two-dimensional geometry, stiffness, and low thermal interface resistance of the GNPs.