The dynamics of closely index matched colloidal crystals of charged silica spheres dispersed in deionized ethylene glycol-water mixture is investigated using dynamic light scattering. At variance with the reports of phonon dispersion measurements on thin colloidal crystals, our observations on millimeter-sized crystals show unambiguous evidence for overdamped transverse modes turning propagative in the range of small wave numbers in agreement with the theory of hydrodynamic interactions in charged colloidal crystals.