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We report precise Doppler velocities of HD 3651 obtained at Lick and Keck Observatories. The velocities reveal evidence of a planetary companion with an orbital period of 62.23 ± 0.03 days, an eccentricity of 0.63 ± 0.04, and a velocity semiamplitude of 15.9 ± 1.7 m s-1. With an assumed mass of 0.79 M for this K0 V star, we derive M sin i = 0.20MJ and a semimajor axis of 0.284 AU. The star is chromospherically inactive, with log R = -5.01, and 10 years of observations at Fairborn Observatory show it to be photometrically stable to better than 0.001 mag. In particular, there is no photometric variability on the 62.23 day radial velocity period to a limit of 0.0002 mag, supporting the planetary interpretation of the radial velocity variability. Photometric transits of the planetary companion across the star are ruled out with a probability of 87%.