  We present the computation of Higgs boson plus one jet production at NNLO at
the LHC. The computation is carried out in the heavy-top-quark approximation
and using the antenna subtraction formalism to handle the IR divergent
structure of the individual contributions. All channels and all colours are
included. We illustrate aspects of the subtraction formalism and present
results for the total cross section as well as distributions in the kinematical
variables using a realistic experimental setting. We make a comparison between
our results and recent ATLAS data for $H+j$ production.
