Compton scattering of laser light by an electron beam at large angles,
in particular at 90 degrees, produces coherent hard radiation if the
density of the electron beam is high enough. In this case, the intensi
ty of the scattered radiation is greatly enhanced in a small cone arou
nd the forward direction of propagation of the electron beam. As an ex
ample, the production of 1-KeV coherent X rays is discussed.