Our ab initio theoretical calculations indicate that the LiFLi- anion possesses two bound states which are of (1) Sigma(g)(+) and (3) Sigma(u)(+) symmetry and which have vertical detachment energies of 0.94 and 0.89 eV, respectively. The LiFLi+ cation and the first four electronic states of the neutral LiFLi were also considered. The Renner-Teller splitting for the excited (2) Pi(u) state of the neutral is reported. The neutral and both ions are thermodynamically stable.