We use molecular dynamics simulations to study the shear flow of a polymer solution in a nanochannel by using an explicit, atomistic model of the solvent. The length scales representing the chain size, channel size, and the molecular scale structure in these nanochannels are comparable. The diffusion and hydrodynamic interactions in the system are governed by the intermolecular interactions in the explicit solvent model that is used in the simulations. We study the cross stream migration of flexible polymer chains in a solution that is subjected to a planar Couette flow in a nanochannel. We present a detailed study of the effects of chain length, channel size, and solution concentration on the cross stream chain migration process. Our results show that when a dilute solution containing a longer and a shorter chain is subjected to shear flow, the longer chains that are stretched by the flow migrate away from the channel walls, while the shorter chains that do not stretch also do not exhibit this migration behavior. The thickness of the chain depletion layer at the channel surface resulting from cross stream migration is found to increase with an increase in the channel height. On the other hand, this degree of migration away from the channel walls is found to decrease with an increase in the solution concentration. In solutions with concentrations comparable to or greater than the overlap concentration, the depletion layer thickness in shear flow is found to be comparable or slightly smaller than that observed in the absence of flow.