The white dwarf LHS 3236 (WD1639+153) is shown to be a double-degenerate binary, with each component having a high mass. Astrometry at the U.S. Naval Observatory gives a parallax and distance of 30.86 ± 0.25 pc and a tangential velocity of 98 km s-1, and reveals binary orbital motion. The orbital parameters are determined from astrometry of the photocenter over more than three orbits of the 4.0 yr period. High-resolution imaging at the Keck Observatory resolves the pair with a separation of 31 and 124 mas at two epochs. Optical and near-IR photometry give a set of possible binary components. Consistency of all data indicates that the binary is a pair of DA stars with temperatures near 8000 and 7400 K and with masses of 0.93 and 0.91 M ; also possible is a DA primary and a helium DC secondary with temperatures near 8800 and 6000 K and with masses of 0.98 and 0.69 M . In either case, the cooling ages of the stars are ∼3 Gyr and the total ages are <4 Gyr. The combined mass of the binary (1.66-1.84 M ) is well above the Chandrasekhar limit; however, the timescale for coalescence is long.