BICEP3 is a 550 mm-aperture refracting telescope for polarimetry of radiation in the cosmic microwave background at 95 GHz. It adopts the methodology of BICEP1, BICEP2 and the Keck Array experiments - it possesses sufficient resolution to search for signatures of the inflation-induced cosmic gravitational-wave background while utilizing a compact design for ease of construction and to facilitate the characterization and mitigation of systematics. However, BICEP3 represents a significant breakthrough in per-receiver sensitivity, with a focal plane area 5$times$ larger than a BICEP2/Keck Array receiver and faster optics ($f/1.6$ vs. $f/2.4$). Large-aperture infrared-reflective metal-mesh filters and infrared-absorptive cold alumina filters and lenses were developed and implemented for its optics. The camera consists of 1280 dual-polarization pixels; each is a pair of orthogonal antenna arrays coupled to transition-edge sensor bolometers and read out by multiplexed SQUIDs. Upon deployment at the South Pole during the 2014-15 season, BICEP3 will have survey speed comparable to Keck Array 150 GHz (2013), and will significantly enhance spectral separation of primordial B-mode power from that of possible galactic dust contamination in the BICEP2 observation patch.