We present a deep ASCA observation of a Broad Absorption Line Quasar (BALQSO) PG0946+301. The source was clearly detected in one of the gas imaging spectrometers, but not in any other detector. If BALQSOs have intrinsic X-ray spectra similar to normal radio-quiet quasars, our observations imply that there is Thomson thick X-ray absorption (N_H >~10^{24} cm^{-2}) toward PG0946+301. This is the largest column density estimated so far toward a BALQSO. The absorber must be at least partially ionized and may be responsible for attenuation in the optical and UV. If the Thomson optical depth toward BALQSOs is close to one, as inferred here, then spectroscopy in hard X-rays with large telescopes like XMM would be feasible.