Deep near-infrared CCD imaging of the field of the recently discovered nearby galaxies Dwingeloo 1 and 2 has revealed a third, previously unknown galaxy which is most likely a second physical companion of Dwingeloo 1. Only 9'.2 to the southwest of Dwingeloo 1 is a diffuse featureless oval with a diameter of 1'.9 in I. Isophotes are oriented nearly east-west and within 30 degrees of the direction of Dwingeloo 1. Neutral hydrogen studies have failed to reveal a source at this position, and no H alpha emission is evident. Thus, the object is probably a dwarf spheroidal companion of Dwingeloo 1, although there is a small possibility that it is a quiescent gas-rich dwarf with a velocity low enough that its signal is confused with emission from the Milky Way. The galaxy is almost certainly a member of the IC 342-Maffei 1 group, thereby placing it 3+/-1 Mpc away. (C) 1997 American Astronomical Society.