We present the cross section for production of a Z boson in association with four jets at the Large Hadron Collider, at next-to-leading order in the QCD coupling. When the Z decays to neutrinos, this process is a key irreducible background to many searches for new physics. Its computation has been made feasible through the development of the on-shell approach to perturbative quantum field theory. We present the total cross section for pp collisions at \sqrt{s} = 7 Tev, after folding in the decay of the Z boson, or virtual photon, to a charged-lepton pair. We also provide distributions of the transverse momenta of the four jets, and we compare sections and distributions to the corresponding ones for the production of a W boson with accompanying jets. Show Partial Abstract