We report the detection of the lowest mass extrasolar planet yet found around a Sun-like star—a planet with an M sin i of only 14.21±2.91 M⊕ in an extremely short period orbit (P= 2.808 days) around ρ 1 Cancri, a planetary system that already has three known planets. Velocities taken from late 2003-2004 at McDonald Observatory with the Hobby-Eberly Telescope revealed this inner planet at 0.04 AU. We estimate an inclination of the outer planet ρ 1 Cancri d, based on Hubble Space Telescope Fine Guidance Sensor measurements that suggest an inner planet of only 17.7±5.57 M⊕, if coplanarity is assumed for the system.