Infrared reflectivity measurements have been made at 78°K on three samples of GaAs, doped with Te so that the plasma frequency is nearly equal to the long-wavelength LO phonon frequency. There are two prominent dips in the reflectivity spectra, but instead of occurring near the plasma frequency and LO mode frequency, they occur at the frequencies of the two normal modes of the coupled plasmon-LO-phonon system, as predicted by Varga and by Singwi and Tosi. From the reflectivity spectra at 78°K, values of the electron effective mass of 0.067, 0.073, and 0.077me are obtained for n-type GaAs with 7.22×1017, 8.75×1017, and 14.0×1017 carriers per cm3.