We have analyzed archival Einstein Observatory images of a roughly 4.5 square degree region centered on the Orion Nebula. In all, 245 distinct X-ray sources have been detected in six High Resolution Imager (HRI) and 17 Imaging Proportional Counter (IPC) observations. An optical database of over 2700 stars has been assembled to search for candidate counterparts to the X-ray sources. Roughly half the X-ray sources are identified with a single Orion Nebula cluster member. The 10 main-sequence O6-B5 cluster stars detected in Orion have X-ray activity levels comparable to field O and B stars. X-ray emission has also been detected in the direction of four main-sequence late-B and early-A type stars. Since the mechanisms producing X-rays in late-type coronae and early-type winds cannot operate in the late-B and early-A type atmospheres, we argue that the observed X-rays, with L_X_~3x10^30^ergs/s, are probably produced in the coronae of unseen late-type binary companions. Over 100 X-ray sources have been associated with late-type pre-main sequence stars.