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 HT , are provided for the initial LHC energy of ps = 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. Show Partial Abstract