A biased Monte Carlo method is developed to simulate shear flow of linear homopolymers between neutral hard walls.. Simulations are conducted on a face- centered cubic (FCC) lattice at full occupancy (phi = I) using a modified version of cooperative motion (COMOTION) algorithm. As chain lengths are increased under quiescent conditions, a clear crossover in chain dynamics from Rouse behavior to reptation-like behavior is revealed in characteristic correlation functions. Shear flow is simulated through the use of a biasing technique that favors segmental movement in the A direction of flow; this combination of cooperative motion with flow is referred to as the COMOFLO algorithm. Using this technique, rheological properties are calculated as a function of shear rate and chain length. The viscosity and the first and second normal stress coefficients are calculated and found to be consistent with well established experimental facts. The zero shear viscosity scales linearly with low molecular weights (eta(0) similar to N-1.0) and scales to the 3.5 power at higher molecular weights (eta(0) similar to N-3.5). This crossover in viscosity scaling occurs at the same chain lengths (N similar to 150) as the transition in chain dynamics Because the simulations are conducted in the athermal limit, there are no parameter inputs. The known observable linear viscoelastic rheological properties of polymer melts are thus predicted in an a priori fashion.