Using an ab initio, nonlocal pseudopotential method, we have calculated the reflectance anisotropy spectrum for a particular model of the GaAs(001) c(4x4) reconstructed surface. Excellent agreement with experiment was obtained, supporting the chosen model. The reflectance anisotropy was found to originate from optical transitions between bulk like valence band states and surface states in the conduction band. The nature and distribution of the electronic states involved is discussed.