  We report on the first next-to-leading order QCD computation of W + 3-jet
production in hadronic collisions including all partonic subprocesses. We
compare the results with CDF data from the Tevatron, and find excellent
agreement. The renormalization and factorization scale dependence is reduced
substantially compared to leading-order calculations. The required one-loop
matrix elements are computed using on-shell methods, implemented in a numerical
program, BlackHat. We use the SHERPA package to generate the real-emission
contributions and to integrate the various contributions over phase space. We
use a leading-color (large-N_c) approximation for the virtual part, which we
confirm in W + 1,2-jet production to be valid to within three percent. The
present calculation demonstrates the utility of on-shell methods for computing
next-to-leading-order corrections to processes important to physics analyses at
the Large Hadron Collider.
