The frontier orbital sequence of individual dicyanovinyl-substituted oligothiophene molecules is studied by means of scanning tunneling microscopy. On NaCl/Cud(111), the molecules are neutral, and the two lowest unoccupied molecular states are observed in the expected order of increasing energy. On NaCl/Cud(311), where the molecules are negatively charged, the sequence of two observed molecular orbitals is reversed, such that the one with one more nodal plane appears lower in energy. These experimental results, in open contradiction with a single-particle interpretation, are explained by a manybody theory predicting a strongly entangled doubly charged ground state.