W+3 jet production at the Tevatron

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% which is a significant improvement compared to the leading order result.