We report on the discovery of a supermassive binary black hole system in the radio galaxy 0402+379, with a projected separation between the two black holes of just 7.3 pc. This is the closest black hole pair yet found by more than two orders of magnitude. These results are based upon recent multi-frequency observations using the Very Long Baseline Array (VLBA) which reveal two compact, variable, flat-spectrum, active nuclei within the elliptical host galaxy of 0402+379. Multiepoch observations from the VLBA also provide constraints on the total mass and dynamics of the system. Low spectral resolution spectroscopy using the Hobby-Eberly Telescope indicates two velocity systems with a combined mass of the two black holes of 1.5 108 M . 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 close binary black holes that might be sources of gravitational radiation. Green Bank Telescope observations at 22 GHz to search for water masers in this interesting system are also presented.