We report the appearance of a new radio source at a projected offset of 460 pc from the nucleus of Cygnus A. The flux density of the source (which we designate Cygnus A-2) rose from an upper limit of <0.5 mJy in 1989 to 4 mJy in 2016 ( = 8.5 GHz), but is currently not varying by more than a few percent per year. The radio luminosity of the source is comparable to the most luminous known supernovae, it is compact in Very Long Baseline Array observations down to a scale of 4 pc, and it is coincident with a near-infrared point source seen in pre-existing adaptive optics and HST observations. The most likely interpretation of this source is that it represents a secondary supermassive black hole in a close orbit around the Cygnus A primary, though an exotic supernova model cannot be ruled out. The gravitational influence of a secondary SMBH at this location may have played an important role in triggering the rapid accretion that has powered the Cygnus A radio jet over the past 107 years.