We report the first observation of interference in charge exchange collisions between two ions. Employing the crossed-beams technique in conjunction with signal recovery methods, angular differential cross sections have been measured for charge transfer in He{sup 2+}+He {sup +} collisions at barycentric energies between 0.5 and 10.2keV. The oscillatory structure observed is in agreement with quantum calculations and can be interpreted in terms of interference between scattering into {ital gerade} and {ital ungerade} molecular states, which arise due to the identity of the nuclear charges. {copyright} {ital 1997} {ital The American Physical Society}