We investigated the localized rotational diffusion of the (BH4)(-) anions in LiBH4/LiI solid solutions by means of quasielastic and inelastic neutron scattering. The (BH4)(-) motions are thermally activated and characterized by activation energies in the order of 40 meV. Typical dwell times between jumps are in the picosecond range at temperatures of about 200 K. The motion is dominated by 90 degrees reorientations around the 4-fold symmetry axis of the tetrahedraly shaped (BH4)(-) ions. As compared to the pure system, the presence of iodide markedly reduces activation energies and increases the rotational frequencies by more than a factor of 100. The addition of iodide lowers the transition temperature, stabilizing the disordered high temperature phase well below room temperature.