The G0 V star 47 UMa exhibits very low amplitude radial velocity variations having a period of 2.98 yr, a velocity amplitude of K = 45.5 m s-1, and small eccentricity. The residuals scatter by 11 m s-1 from a Keplerian fit to the 34 velocity measurements obtained during 8 yr. The minimum mass of the unseen companion is M2 sin i = 2.39 MJ, and for likely orbital inclinations of 30 deg--90 deg, its mass is less than 4.8 MJ. This mass resides in a regime associated with extrasolar giant planets (Burrows and coworkers). Unlike the planet candidates 70 Vir B and 51 Peg B, this companion has an orbital radius (2.1 AU) and eccentricity (e = 0.03) reminiscent of giant planets in our solar system. Its effective temperature will be at least 180 K due simply to absorbed stellar radiation, and probably slightly higher due to intrinsic heating from gravitational contraction (Guillot and coworkers). For 47 UMa B to be, instead, an orbiting brown dwarf of mass M > 40 MJ, the inclination would have to be i < 3.dg4, which occurs for only 0.18% of randomly oriented orbits. In any case, this companion is separated from the primary star by ~0."2, which portends follow-up work by astrometric and direct IR techniques.