The topological properties of lead-tin chalcogenide topological crystalline insulators can be widely tuned by temperature and composition. It is shown that bulk Bi doping of epitaxial Pb<sub>1-sub><sub>xsub>Sn<sub>xsub>Te (111) films induces a giant Rashba splitting at the surface that can be tuned by the doping level. Tight binding calculations identify their origin as Fermi level pinning by trap states at the surface.