  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
semi-amplitude of $K =18.1$ \ms. The minimum mass (\msini) for the planet is
0.067 \mjup = 1.2 M$_{\rm NEP}$ = 21 M$_{\rm EARTH}$, 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 \msune) 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 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 IR
