IRAS 09104 + 4109 is the most luminous object yet discovered by means of the IRAS survey. It is identified with a cD galaxy having a strong emission-line spectrum at a redshift of 0.442 and emits 6 x 10 to the 12th solar luminosities/sq h, 99 percent of which emerges at infrared wavelengths. One component of a double radio source is coincident with the center of the galaxy. The high luminosity of this source may be related to an interaction with one or more members of the rich cluster in which it lies. There is a secondary peak in the emission-line image of the galaxy. Emission lines from both regions are broad but narrower than those characteristic of the only other objects known to have such high luminosities, such as Seyfert 1's and QSOs. It is suggested that the strong infrared excess of IRAS 09104 + 4109 is produced by dust obscuring a broad line region.