  We report the discovery of HD 156668b, 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, is among the lowest ever detected,
on par with the detection of GJ 581e using HARPS. A longer period (P ~ 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 ~3 mmag, ruling out
transiting planets dominated by extremely bloated atmospheres, but not
precluding a transiting solid/liquid planet with a modest atmosphere.
