The result of a survey of X-ray emission from luminous early-type stars is reported in which observations were made using the imaging proportional counter on the Einstein Observatory. The survey suggests that all Of stars and OB supergiants earlier than B1 I are X-ray sources with luminosities not less than 10 to the 32nd ergs/s and that some later B supergiants have X-ray luminosities not less than 10 to the 31st ergs/s. The X-ray luminosities are roughly 10 to the -7.2nd of the bolometric luminosities for supergiants earlier than B1 and perhaps a factor of 3 less for later B supergiants. Spectral analysis of the X-rays in conjunction with information on anomalous ionization in the wind from four of the strongest sources implies that the data are not consistent with a model in which the X-rays originate in a thin slab coronal zone at the base of the wind. Constraints on the source of X-rays from B supergiants are derived by combining the X-ray flux information with that on ultraviolet line anomalies.