We report the discovery of PSR J1555-2908, a 1.79ms radio and gamma-ray pulsar in a 5.6hr binary system with a minimum companion mass of 0.052M_{sun}_. This fast and energetic (\dot{E}=3x10^35^erg/s) millisecond pulsar was first detected as a gamma-ray point source in Fermi Large Area Telescope (LAT) sky survey observations. Guided by a steep-spectrum radio point source in the Fermi error region, we performed a search at 820MHz with the Green Bank Telescope that first discovered the pulsations. The initial radio pulse timing observations provided enough information to seed a search for gamma-ray pulsations in the LAT data, from which we derive a timing solution valid for the full Fermi mission. In addition to the discovery and timing of radio and gamma-ray pulsations, we searched for X-ray pulsations using NICER but no significant pulsations were detected. We also obtained time-series r-band photometry that indicates strong heating of the companion star by the pulsar wind. Material blown off the heated companion eclipses the 820MHz radio pulse during inferior conjunction of the companion for ~10% of the orbit, which is twice the angle subtended by its Roche lobe in an edge-on system.