The Primordial Inflation Polarization Explorer (PIPER) is a balloon-borne instrument that will probe the epoch of reionization and search for the signature of inflation through large angular scale measurements of the linear polarization of the cosmic microwave background in four frequency bands from 200 to 600 GHz. It consists of twin co-pointed telescopes cooled to 1.5 K within an open liquid helium bucket dewar. Variable-delay polarization modulators chop between linear and circular polarization to provide sensitivity to the full IQUV polarization state within each sky pixel. A pair of 32 x 40 element detector arrays provides background-limited sensitivity at bolometric loading comparable to a space mission. PIPER is now fully integrated; we discuss the sky coverage, sensitivity, and science goals expected from the planned series of flights.