Weakly damped lower hybrid wave propagation is shown to be chaotic for parameter regimes typical of current drive in TORE SUPRA and IT-60. In these cases, the spectral gap is filled by wave energy that diffuses to higher parallel wavenumber k// in the stochastic layer. Agreement between theoretical and experimental scalings for the current drive efficiency is obtained by including nonresonant losses of wave energy due to collisions and loss reflections near the plasma edge which reduce the efficiency at low temperatures when the spectral gap is large