Room-temperature single-electron transistors are realized within individual metallic single-wall carbon nanotube molecules. The devices feature a short (down to approximately 20 nanometers) nanotube section that is created by inducing local barriers into the tube with an atomic force microscope. Coulomb charging is observed at room temperature, with an addition energy of 120 millielectron volts, which substantially exceeds the thermal energy. At low temperatures, we resolve the quantum energy levels corresponding to the small island. We observe unconventional power-law dependencies in the measured transport properties for which we suggest a resonant tunneling Luttinger-liquid mechanism.