Dielectric response of hen egg white lysozyme is measured in the far infrared (5-65 cm-1, 0.15-1.95 THz, 0.6-8.1 meV) as a function of hydration. The frequency range is associated with collective vibrational modes of protein tertiary structure. The observed frequency dependence of the absorbance is broad and glass-like. For the entire frequency range, there is a slight increase in both the absorbance and index of refraction with increasing hydration for <0.27 h (mass of H2O per unit mass protein). At 0.27 h, the absorbance and index begin to increase more rapidly. This transition corresponds to the point where the first hydration shell is filled. The abrupt increase in dielectric response cannot be fully accounted for by the additional contribution to the dielectric response due to bulk water, suggesting that the protein has not yet achieved its fully hydrated state. The broad, glass-like response suggests that at low hydrations, the low frequency conformational hen egg white lysozyme dynamics can be described by a dielectric relaxation model where the protein relaxes to different local minima in the conformational energy landscape. However, the low frequency complex permittivity does not allow for a pure relaxational mechanism. The data can best be modeled with a single low frequency resonance (nu approximately 120 GHz=4 cm-1) and a single Debye relaxation process (tau approximately .03-.04 ps). Terahertz dielectric response is currently being considered as a possible biosensing technique and the results demonstrate the required hydration control necessary for reliable biosensor applications.