A single 3.5 hour observation on 1979 March 6 with the imaging proportional counter aboard the Einstein Observatory has revealed the presence of numerous low-luminosity (10 to the 31st ergs/s) X-ray sources in a region centered near the Trapezium in the Orion Nebula. In addition to the Trapezium, 22 discrete sources have been detected in a 1 x 1 deg field at or above the 4 sigma level. These sources are clearly associated with star formation, as indicated by the similarity of their spatial distribution with that of the nebular variables, a class of pre-main-sequence stars. Because the field is quite crowded, however, individual identifications of these sources are difficult. In addition to the discrete sources, there is evidence for diffuse or unresolved emission from two ridges extending 16 deg to the north and 15 deg to the west of the Trapezium. The nature of the discrete sources and of the diffuse emission is discussed.