X-ray observations of the nearby cluster Abell 1367 were made with the Imaging Proportional Counter (IPC) and High Resolution Imager (HRI) aboard the Einstein Observatory. The IPC is used to study the diffuse cluster emission. With the HRI, eight point sources are detected above the diffuse cluster emission, three of which are apparently associated with cluster galaxies. In addition, the HRI observations have resolved 13 extended features with characteristic radii of order arcmin, eight of which are associated with cluster galaxies. These extended sources have luminosities of 1.5-6.5 x 10 to the 41st per (H0)50)-squared ergs per sec in the 0.5-4.5 keV band and constitute about 60% of the total cluster emission. The ways in which these hot galactic coronae can be maintained are discussed.