The titanium boride cation system, TiB+, has been examined by ab initio MRCI (CASSCFS1+2) methods. In addition to the ground, X(5)Delta state, 23 low-lying excited states are reported with symmetries (1,3)Sigma(+), (1,3,5)Sigma(-), (1,3,5)Pi (1,3,5)Delta, (1,3,5)Phi, and (1,3,5)Gamma, spanning an energy range of 35 kcal/mol. All reported states are bound with respect to the ground state atoms Ti+(a(4)F) + B(P-2), with binding energies ranging from 47.6 (X(5)Delta) to 13.8 (23(1)Pi) kcal/mol. The state with the highest internal bond strength (120 kcal/mol) and the shortest bond length (1.866 Angstrom) is the first excited (1)Sigma(+) state, binding via a "genuinely" triple bond. For all states studied we report total energies, bond lengths, harmonic frequencies, and full potential energy curves, while an effort has been made to interpret bonding interactions by employing simple valence-bond diagrams.