A well-dispersed phase of exfoliated graphene oxide (GO) nanosheets was initially prepared in water. This was concentrated by centrifugation and was mixed with a liquid epoxy resin. The remaining water was removed by evaporation, leaving a GO dispersion in epoxy resin. A stoichiometric amount of an anhydride curing agent was added to this epoxy-resin mixture containing the GO nanosheets, which was then cured at 90 °C for 1 h followed by 160 °C for 2 h. A second thermal treatment step of 200 °C for 30 min was then undertaken to reduce further the GO in situ in the epoxy nanocomposite. An examination of the morphology of such nanocomposites containing reduced graphene oxide (rGO) revealed that a very good dispersion of rGO was achieved throughout the epoxy polymer. Various thermal and mechanical properties of the epoxy nanocomposites were measured, and the most noteworthy finding was a remarkable increase in the thermal conductivity when relatively very low contents of rGO were present. For example, a value of 0.25 W/mK was measured at 30 °C for the nanocomposite with merely 0.06 weight percentage (wt%) of rGO present, which represents an increase of ~40% compared with that of the unmodified epoxy polymer. This value represents one of the largest increases in the thermal conductivity per wt% of added rGO yet reported. These observations have been attributed to the excellent dispersion of rGO achieved in these nanocomposites made via this facile production method. The present results show that it is now possible to tune the properties of an epoxy polymer with a simple and viable method of GO addition.