Evidence for the rapid internal rotation of the sun obtained from Doppler shift measurements of the Fraunhofer absorption lines is reported. An improved version of the Doppler shift optical resonance spectrometer was used to record the resonantly scattered intensities corresponding to the two wings of the 769.9-nm Fraunhofer absorption lines of neutral potassium on 28 continuous days in July and August 1980. A total of 33 lines was identified which were found to be split into components corresponding to the l = 1, l = 2 and l = 0 modes of the spherical harmonic. Superposed frequency spectra for each mode exhibit a width indicative of high-Q oscillations, with a mean value of 0.75 microHz. Comparison of this value with that anticipated for the case of uniform rotation (0.4 microHz) reveals that the core of the sun rotates two to nine times as rapidly as the surface.