Proton transport along water chains is thought to be essential for the translocation of protons over large distances in proteins. In this paper the real-time nonequilibrium quantum dynamics of proton transport along chains of three or four water molecules is simulated using the multiconfigurational molecular dynamics with quantum transitions method. A linearly increasing external electric field is applied to the water chain to model the field exerted by a protein, and restraints are applied to the oxygen atoms to model the structural constraints of the protein. The simulations indicate that fluctuating electric fields and structural constraints strongly affect the dynamics of proton transport along water chains. In addition, quantum mechanical effects such as hydrogen tunneling and nonadiabatic transitions play an important role under certain nonequilibrium conditions.