Ab initio electronic structure calculations on several low-lying valence states of B3 have been carried out using correlation-consistent polarized valence double-zeta basis sets and complete-active-space self-consistent field treatments of electron correlation. Stable triangular structures, linear structures, and Jahn-Teller unstable structures are all observed. Equilibrium geometries, energies, and local harmonic vibrational frequencies are determined for various locally stable structures of several states. Several of the local minima are found to be unstable or metastable when zero-point vibrational energy is included; as a result, fluxional species are predicted to occur for certain B3 states. Transition states connecting local minima are found and characterized in terms of energies, geometries, and local harmonic vibrational frequencies. The ground state of B3 is predicted to have an equilateral triangular structure and to be of 2A 1' symmetry in the D3h point group. Dipole and vibronically allowed vertical transition energies to other states are also considered.