We demonstrate how the frequency of a single-mode cw dye laser can be translated by 1.772 GHz using stimulated Raman scattering in sodium vapor. The output of a sodium Raman laser, the frequency-translated beam, is shown to be highly correlated in frequency with the dye-laser pump beam. The bandwidth of the 1.772-GHz heterodyne beat signal between the two beams is found to be as narrow as 440 Hz, much narrower than the root-mean-square frequency jitter (approximately 1 MHz) of the dye-laser pump beam. The Raman laser method can be used with materials other than sodium, such as cesium or magnesium, to obtain frequency translations of a magnitude that may not be easily attainable with acousto-optic or electro-optic techniques.