We present the observation of optomechanical coupling in crystalline whispering-gallery-mode (WGM) resonators. The high purity of the material enables optical quality factors in excess of 10(10) and finesse exceeding 10(6), as well as mechanical quality factors greater than 10(5). Ultrasensitive displacement measurements reveal mechanical radial modes at frequencies up to 20 MHz, corresponding to unprecedentedly high sideband factors (>100). In combination with the weak intrinsic mechanical damping this renders crystalline WGM microresonators promising for experiments in the classical and quantum regime of optomechanics.