  We compute the cross section and differential distributions for the
production of a Standard Model Higgs boson in association with a hadronic jet
to next-to-next-to-leading order in quantum chromodynamics (QCD). In Higgs
boson studies at the LHC, final states containing one jet are a dominant
contribution to the total event rate, and their understanding is crucial for
improved determinations of the Higgs boson properties. We observe substantial
higher order corrections to transverse momentum spectra and rapidity
distributions in Higgs-plus-one-jet final states. Their inclusion stabilises
the residual theoretical uncertainty of the predictions around 9\%, thereby
providing important input to precision studies of the Higgs boson.
