X-ray emission from a contact binary star was first detected by the HEAO 1 satellite in 1977. Spectroscopic observations of 44i Boo and VW Cep by IUE established the presence of high-temperature chromospheric and transition region emission lines in the spectra of these stars. The HEAO 1 and IUE results implied that the processes causing X-ray emission from VW Cep might be similar to those energizing the solar corona, and that X-ray emission might be a common occurrence among contact binary stars. A series of observations of these stars was, therefore, conducted with the aid of the HEAO 2 (Einstein) Observatory. The present investigation is concerned with the results of these observations, giving attention to their implications with respect to the nature of contact binary stars. The results are compared with similar HEAO 2 studies of coronal X-ray sources in the local region of the Galaxy, in the Hyades, and other rapidly rotating systems.