The local structure of the highly "overdoped" 95 K superconductor Sr2CuO3.3 determined by Cu K X-ray absorption fine structure (XAFS) at 62 K in magnetically oriented samples shows that 1) the magnetization is perpendicular to the c axis; 2) at these levels of precision the Cu sublattice is tetragonal in agreement with the crystal structure; the O sublattice has 3) continuous -Cu-O- chains that orient perpendicular to an applied magnetic field; 4) approximately half-filled -Cu-O- chains that orient parallel to this field; 5) a substantial number of apical O vacancies; 6) O ions at some apical positions with expanded Cu-O distances; and 7) interstitial positions that imply highly displaced Sr ions. These results contradict the universally accepted features of cuprates that require intact CuO2 planes, magnetization along the c axis, and a termination of the superconductivity when the excess charge on the CuO2 Cu ions exceeds 0.27. These radical differences in charge and structure demonstrate that this compound constitutes a separate class of Cu-O-based superconductors in which the superconductivity originates in a different, more complicated structural unit than CuO2 planes while retaining exceptionally high transition temperatures.