By dispersing laser-induced fluorescence (LIF) due to transitions from bent, excited LiOLi (B-1(1), K' = 1) rovibrational states to linear ground-state LiOLi[(X) over tilde (1)Sigma (+)(g)(v " (1), v " (2), v " (3),)] vibrational states, we have determined 37 (v " (1), v " (2), v " (3)) vibrational eigenstate energies, each to an accuracy of about +/-10 cm(-1). An eight-term power series fit of the energies results in estimates of the omega " (1), omega " (2), omega " (3) fundamental frequencies, the chi " (11), chi " (22) anharmonicity constants, and the chi " (12), chi " (23), chi " (13) coupling constants. For such a strongly bound ionic molecule (Li1+O2-Li1+), LiOLi is remarkably floppy, with a 'light-atom' omega " (2) bending frequency of only 122 +/- 4 cm(-1).