Three-crystal X-ray diffractometry (TCD) in grazing Bragg-Laue geometry has been experimentally realized for the first time. Theoretical simulations for the angular position and intensity of the main peak and the pseudopeak on TCD spectra have been obtained. It was established that TCD in grazing Bragg-Laue geometry has the following peculiarities: (1) the angular position and intensity of the main peak on the spectra depend on the sign of the deviation angle; (2) the main peak vanishes completely at negative deviation angles reaching the critical value; (3) the intensity of the main peak in grazing Bragg-Laue geometry is increased approximately by a factor of 102 (compared to symmetrical Bragg diffraction geometry). The above peculiarities were predicted theoretically and confirmed by experimental studies on ideal Si crystals.