We report the discovery of HD 156668 b , an extrasolar planet with a minimum mass of M _ { P } \sin i = 4.15 M _ { \earth } . This planet was discovered through Keplerian modeling of precise radial velocities from Keck-HIRES and is the second super-Earth to emerge from the NASA-UC Eta-Earth Survey . The best-fit orbit is consistent with circular and has a period of P = 4.6455 d. The Doppler semi-amplitude of this planet , K = 1.89 m s ^ { -1 } , is among the lowest ever detected , on par with the detection of GJ 581 e using HARPS . A longer period ( P \approx 2.3 yr ) , low-amplitude signal of unknown origin was also detected in the radial velocities and was filtered out of the data while fitting the short-period planet . Additional data are required to determine if the long-period signal is due to a second planet , stellar activity , or another source . Photometric observations using the Automated Photometric Telescopes at Fairborn Observatory show that HD 156668 ( an old , quiet K3 dwarf ) is photometrically constant over the radial velocity period to 0.1 mmag , supporting the existence of the planet . No transits were detected down to a photometric limit of \sim 3 mmag , ruling out transiting planets dominated by extremely bloated atmospheres , but not precluding a transiting solid/liquid planet with a modest atmosphere .