In most polymer processing conditions, the shear rate experienced by the polymer is faster than the inverse of the relaxation time of the polymer chains. It is well known that, on the average, polymer chains orient along the flow direction under these conditions. If we look at each polymer chain, however, we will find that the chain does not orient statically but is rotating even under steady shear flow. Understanding how they rotate would give us useful information for controlling the orientation of chains in the products. In this paper, we use two molecular simulations (a slip-link model, which is a highly course-grained model of entangled polymers, and a molecular dynamics simulation) to study the rotation of polymer chains under fast shear flow. Under equilibrium (no flow) condition, each polymer chain slowly and randomly rotates by reptation, but average numbers of positive (clockwise) and negative (counter clockwise) rotations per unit time are equal and there is no net rotation. If slow shear flow is applied, the net rotation per unit time is found to be proportional to and of the order of the shear rate. If, however, the shear rate exceeds the inverse of the relaxation time, then both simulation methods give an interesting result; the net rotation frequency becomes proportional to the square root of the shear rate. Under fast flow, each chain rotates not continuously but only intermittently, spending long time in a quasi-stationary and highly oriented state. Thus the rotation frequency becomes much slower than the shear rate.