  We compute the cross section and differential distributions for the
production of a Z boson in association with a hadronic jet to
next-to-next-to-leading order (NNLO) in perturbative QCD, including the
leptonic decay of the Z boson. We present numerical results for the transverse
momentum and rapidity distributions of both the Z boson and the associated jet
at the LHC. We find that the NNLO corrections increase the next-to-leading
order (NLO) predictions by approximately 1% and significantly reduce the scale
variation uncertainty.
