We present 12 years of precision Doppler data for the very nearby G3 star HD 102365, which reveals the presence of a Neptune-like planet with a 16.0 M Earth minimum mass in a 122.1 day orbit. Very few "Super Earth" planets have been discovered to date in orbits this large and those that have been found reside in multiple systems of between three and six planets. HD 102365 b, in contrast, appears to orbit its star in splendid isolation. Analysis of the residuals to our Keplerian fit for HD 102365 b indicates that there are no other planets with minimum mass above 0.3 M Jup orbiting within 5 AU and no other "Super Earths" more massive than 10 M Earth orbiting at periods shorter than 50 days. At periods of less than 20 days these limits drop to as low as 6 M Earth. There are now 32 exoplanets known with minimum mass below 20 M Earth, and interestingly the period distributions of these low-mass planets seem to be similar whether they orbit M-, K-, or G-type dwarfs.Based on observations obtained at the Anglo-Australian Telescope, Siding Spring, Australia.