  We compute the next-to-leading order QCD corrections to the production of W
bosons in association with three jets at the Tevatron in the leading color
approximation, which we define by considering the number of colors and the
number of light flavors as being of the same order of magnitude. The
theoretical uncertainty in the next-to-leading order prediction for the
cross-section is of the order of 15-25 percent which is a significant
improvement compared to the leading order result.
