Rotation of the spin of cold neutrons passing through a noncentrosymmetric single crystal is observed. This effect is caused by the Schwinger interaction of the magnetic moment of a moving neutron with the crystalline electric field in a noncentrosymmetric single crystal and depends both on the direction of neutron trajectory in the crystal and on its energy. It is shown that the characteristic magnitude of the effect for α-quartz is ≃(1-2) × 10-4 rad/cm over a wide wavelength range (from 2.8 to 5.5 Å) and is determined by the degree of beam monochromaticity [Δλ/λ = (2-5) × 10-2 in our experiment]. This magnitude corresponds to an electric field of ≃(0.5-1) × 105 V/cm acting on a neutron. The measured value agrees well with the theoretical calculation. © 2001 MAIK "Nauka/Interperiodica".