We present an idea for creation of a crystalline undulator and report its first realization. One face of a silicon crystal was given periodic microscratches (grooves) by means of a diamond blade. The x-ray tests of the crystal deformation due to a given periodic pattern of surface scratches have shown that a sinusoidal-like shape is observed on both the scratched surface and the opposite (unscratched) face of the crystal; that is, a periodic sinusoidal-like deformation goes through the bulk of the crystal. This opens up the possibility for experiments with high-energy particles channeled in a crystalline undulator, a novel compact source of radiation.