X radiation by 900 MeV electrons in accurately aligned 1–100 layers of 16 μm thick monocrystalline foils of Si was measured. We found intense and well collimated monochromatic photons, i.e. self-diffracted X rays (SDX), emitted to the “Bragg angle”. The intensity of SDX was much greater than the parametric X rays from a Si plate of equivalent thickness. For 35.5 keV X rays with 100 layered Si target, absolute brightness of SDX was comparable to the synchrotron radiation from a 1.7 GeV storage ring.