We report the discovery of energetic neutral hydrogen atoms (ENAs) emitted during the X9 solar event of 2006 December 5. Beginning ~1 hr following the onset of this E79 flare, the Low Energy Telescopes (LETs) on both the STEREO A and B spacecraft observed a sudden burst of 1.6-15 MeV protons beginning hours before the onset of the main solar energetic particle event at Earth. More than 70% of these particles arrived from a longitude within ±10° of the Sun, consistent with the measurement resolution. The derived emission profile at the Sun had onset and peak times remarkably similar to the GOES soft X-ray profile and continued for more than an hour. The observed arrival directions and energy spectrum argue strongly that the particle events < 5 MeV were due to ENAs. To our knowledge, this is the first reported observation of ENA emission from a solar flare/coronal mass ejection. Possible origins for the production of ENAs in a large solar event are considered. We conclude that the observed ENAs were most likely produced in the high corona and that charge-transfer reactions between accelerated protons and partially stripped coronal ions are an important source of ENAs in solar events.