We report on the discovery of a supermassive binary black-hole (SBBH) system in the radio galaxy 0402+379, with a projected separation between the two black holes of just 7.3 pc. This is the most compact SBBH pair yet imaged by more than two orders of magnitude. These results are based upon multi-frequency imaging using the Very Long Baseline Array (VLBA) which reveal two compact, variable, flat-spectrum, active nuclei within the elliptical host galaxy of 0402+379. Multi-epoch observations from the VLBA also provide constraints on the total mass and dynamics of the system. The two nuclei appear stationary while the jets emanating from the weaker of the two nuclei appear to move out and terminate in bright hot spots. The discovery of this system has implications for the number of compact binary black holes that might be sources of gravitational radiation. The VLBI Imaging and Polarimetry Survey (VIPS) currently underway should discover several more SBBHs.