  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 cross sections and distributions to
the corresponding ones for the production of a W boson with accompanying jets.
