Quasielastic neutron scattering measurements of dry and 35% D2O hydrated amorphous protein powder of C-phycocyanin were made as a function of temperature ranging from 313K down to 100K. The protein is grown from blue-green algae cultured in D2O and is deuterated up to 99%. The scattering is thus dominated by coherent scattering. Within the best energy resolution of the time-of-flight instrument, which is 28 mueV FWHM, the scattering appears entirely elastic. For this reason we are able to extract a coherent Debye-Waller factor by making an independent measurement of the static structure factor. We observe a considerable difference in the q dependence of the Debye-Waller factor between the dry and hydrated proteins; furthermore, there is an interesting temperature dependence of the Debye-Waller factor that is quite different from that predicted for dense hard-sphere liquids.