The discovery and preliminary spectroscopy of the broad absorption line (BAL) QSO 0059-2735 (z/em/ = 1.595), which shows features never seen before in QSO spectra, are described. In addition to very broad high-ionization troughs of C IV and Si IV, it exhibits an extensive system of low ionization absorptions which include saturated lines of Mg II, Al II, and Al III, and broad Fe II features which have clear evidence for absorption from excited fine structure levels up to 0.12 eV. Even more remarkable are the very probable identifications of Fe II absorption by UV multiplets 62, 63, and 64 which require lower level excitations of 1.1 eV and Fe III absorption by the triplet UV 34 from a lower level at 3.7 eV. These are the first reports of absorption from such highly excited levels in any QSO. Detailed studies of this QSO should provide new insight on the Fe II ionization zones in QSOs and place severe constraints on models for BAL QSOs. 31 references.