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We report precise Doppler measurements of GJ 436 (M2.5 V) obtained at Keck Observatory. The velocities reveal a planetary companion with orbital period of 2.644 days, eccentricity of 0.12 (consistent with zero), and velocity semiamplitude of K = 18.1 m s-1. The minimum mass (M sin i) for the planet is 0.067MJup = 1.2MNep = 21MEarth, making it the lowest mass exoplanet yet found around a main-sequence star and the first candidate in the Neptune-mass domain. GJ 436 (mass = 0.41 M☉) is only the second M dwarf found to harbor a planet, joining the two-planet system around GJ 876. The low mass of the planet raises questions about its constitution, with possible compositions of primarily H and He gas, ice/rock, or rock-dominated. The implied semimajor axis is a = 0.028 AU = 14 stellar radii, raising issues of planet formation, migration, and tidal coupling with the star. GJ 436 is more than 3 Gyr old, based on both kinematic and chromospheric diagnostics. The star exhibits no photometric variability on the 2.644 day Doppler period to a limiting amplitude of 0.0004 mag, supporting the planetary interpretation of the Doppler periodicity. Photometric transits of the planet across the star are ruled out for gas giant compositions and are also unlikely for solid compositions. As the third closest known planetary system, GJ 436 warrants follow-up observations by high-resolution optical and infrared imaging and by the Space Interferometry Mission.

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