Résumé : Elastic 13N + 13C cross sections are measured at center-of-mass energies of 8.15, 10.0, and 14.75 MeV, using a radioactive 13N beam and position-sensitive solid-state detectors. The 13N + 13C angular distributions display oscillations beyond 80° and even a significant rise at large angles for the two higher energies. These data are analyzed in the framework of the optical model including a parity-dependent term necessary to explain the backward behavior. This parity term is among the strongest encountered in heavy-ion collisions. Its properties are close to those of the parity term reproducing the 13N + 12C elastic scattering in the same energy range. Its long-range nature indicates that the parity dependence arises from a single rather than from a double exchange. One-pion charge exchange between the valence nucleons seems to possess the necessary properties as qualitatively shown by a simple molecular model.