The behavior of confined polymer melts in a shear flow is investigated using molecular dynamics simulations. Polymer molecules are modeled as bead-spring chains that interact via repulsive site-site potentials. The fluid is contained between atomistic walls and shear is imparted by moving the walls in opposite directions to simulate planar Couette flow. Experimental conditions are simulated by maintaining the walls at a constant temperature. The density, velocity, and temperature profiles during shear flow are monitored and compared to those of simple liquids under similar conditions. For the shear rates investigated, polymeric fluids exhibit a much stronger tendency for slip at the wall-fluid interface than simple fluids. The magnitude of slip increases with increasing shear rate. For short chains the magnitude of slip increases with increasing chain length but appears to reach an asymptotic value at approximately the entanglement length. The viscosity increases as the film thickness is decreased, in qualitative agreement with surface forces apparatus experiments. The chains stretch and align in the flow direction when sheared.