Complex angular momentum techniques are applied to the theory of elastic scattering in chemically reactive systems. The Watson-Sommerfeld transformation allows the scattering amplitude to be written as a background integral and a sum over Regge Poles in the right-hand complex plane. It is shown the Regge Poles are restricted to the first quadrant for physically meaningful optical potentials. Neglect of the background integral and all poles except for the one closest to the real axis allows the differential cross section for large scattering angles to be written in terms of a Legendre function of complex degree. The theory agrees with experimental results for the elastic angular distributions of direct and complex reactions. It predicts oscillations and a glory in the backward direction of the angular distributions. The oscillations arise from interference between orbiting or surface waves that propagate around the region of chemical reaction. Measurements of angular distributions at different collision energies can be used to determine a Regge trajectory.