New configuration for generation of the parametric X-ray radiation (PXR) by an ultrarelativistic
electron beam is considered. The beam propagates along the external surface of periodical multilayer structure
(superlattice) while the photons are emitted under the condition of grazing incidence diffraction. PXR spectral
intensity is calculated for this case. It is shown that this specific configuration of the electron beam and
target radiator can be used for the PXR generation in a storage ring. It can allow one to obtain the
monochromatic X-ray beams with the smoothly tuned frequency and the spectral intensity exceeding intensity of the
synchrotron radiation in the narrow spectral ranges.