We report a theoretical study of the electronic structure and optical properties of GaAs nanowires grown in the [111] direction with a hexagonal cross section, based on a tight-binding approach. It is shown that in the nanowires the degeneracy of the light-hole and heavy-hole bands at the Γ-point seen in the bulk material is lifted, and the light-hole state is located above the heavy-hole state, in strong contrast to the prediction by effective mass theory. The imaginary part of the dielectric function of the nanowires is also calculated and the absorption spectra is found to be strongly polarized