We apply "molecular dynamics with quantum transitions" (MDQT), a surface-hopping method previously used only for electronic transitions, to proton transfer in solution, where the quantum particle is an atom. We use full classical mechanical molecular dynamics for the heavy atom degrees of freedom, including the solvent molecules, and treat the hydrogen motion quantum mechanically. We identify new obstacles that arise in this application of MDQT and present methods for overcoming them. We implement these new methods to demonstrate that application of MDQT to proton transfer in solution is computationally feasible and appears capable of accurately incorporating quantum mechanical phenomena such as tunneling and isotope effects. As an initial application of the method, we employ a model used previously by Azzouz and Borgis to represent the proton transfer reaction AH-B reversible arrow A(-)-H+B in liquid methyl chloride, where the AH-B complex corresponds to a typical phenol-amine complex. We have chosen this model, in part, because it exhibits both adiabatic and diabatic behavior, thereby offering a stringent test of the theory. MDQT proves capable of treating both limits, as well as the intermediate regime. Up to four quantum states were included in this simulation, and the method can easily be extended to include additional excited states, so it can be applied to a wide range of processes, such as photoassisted tunneling. In addition, this method is not perturbative, so trajectories can be continued after the barrier is crossed to follow the subsequent dynamics.