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Precision radial velocities from the Automated Planet Finder (APF) and Keck/HIRES reveal an Msin (i) = 18 ± 2 M⊕ planet orbiting the nearby M3V star GJ 687. This planet has an orbital period P = 38.14 days and a low orbital eccentricity. Our Strömgren b and y photometry of the host star suggests a stellar rotation signature with a period of P = 60 days. The star is somewhat chromospherically active, with a spot filling factor estimated to be several percent. The rotationally induced 60 day signal, however, is well separated from the period of the radial velocity variations, instilling confidence in the interpretation of a Keplerian origin for the observed velocity variations. Although GJ 687 b produces relatively little specific interest in connection with its individual properties, a compelling case can be argued that it is worthy of remark as an eminently typical, yet at a distance of 4.52 pc, a very nearby representative of the galactic planetary census. The detection of GJ 687 b indicates that the APF telescope is well suited to the discovery of low-mass planets orbiting low-mass stars in the as yet relatively un-surveyed region of the sky near the north celestial pole.