We report precise Doppler measurements of GJ 436 (M2.5V) obtained at Keck Observatory. The velocities reveal a planetary companion with orbital period of 2.644 d, 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 0.067 MJUP = 1.2 MNEP = 21 MEARTH, 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 semi– major axis is a = 0.028 AU = 14 stellar radii, raising issues of planet formation, migration, and tidal coupling with the star. GJ 436 is> 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 1 Based on observations obtained at the W.M. Keck Observatory, which is operated jointly by the University
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