  We present the first next-to-leading order QCD results for W + 4-jet
production at hadron colliders. Total cross sections, as well as distributions
in the jet transverse momenta and in the total transverse energy H_T are
provided for the initial LHC energy of \sqrt{s} = 7 TeV. We use a leading-color
approximation, known to be accurate to 3% for W production with fewer jets. The
virtual matrix elements and the most complicated real-emission matrix elements
are handled by the BlackHat library, based on on-shell methods. The remaining
parts of the calculation, including the integration over phase space, are
performed by the SHERPA package.
