The Fermi Large Area Telescope (LAT) discovered a new gamma-ray source near the Galactic plane, Fermi J0109+6134, when it flared brightly in 2010 February. The low Galactic latitude (b = -1fdg2) indicated that the source could be located within the Galaxy, which motivated rapid multi-wavelength follow-up including radio, optical, and X-ray observations. We report the results of analyzing all 19 months of LAT data for the source, and of X-ray observations with both Swift and the Chandra X-ray Observatory. We determined the source redshift, z = 0.783, using a Keck Low-Resolution Imaging Spectrometer observation. Finally, we compiled a broadband spectral energy distribution (SED) from both historical and new observations contemporaneous with the 2010 February flare. The redshift, SED, optical line width, X-ray absorption, and multi-band variability indicate that this new GeV source is a blazar seen through the Galactic plane. Because several of the optical emission lines have equivalent width >5 Å, this blazar belongs in the flat-spectrum radio quasar category.