We present a quantum study of a proton transfer reaction AH<--B reversible arrow A(-)-H+B in liquid methyl chloride, where the AH-B complex corresponds to phenol-amine. We use the same intramolecular potentials that were used in two earlier studies of this system [H. Azzouzz and D. Borgis, J. Chem. Phys. 98, 7361 (1993); S. Hammes-Schiffer and J. C. Tully, J. Chem. Phys. 101, 4657 (1994).] The former study employed a Landau-Zener approach and a molecular dynamics centroid method, while the latter a surface-hopping method. These studies obtained results that differ by an order of magnitude. In the present work, we first performed a molecular dynamics simulation to obtain the spectral density, which was then used as an input to the method we have developed for the study of the quantum Kramers problem [S. D. Schwartz, J. Chem. Phys. 105, 6871 (1996)]. Thus, in this work both the reaction coordinate and the bath are treated quantum mechanically.