  We present numerical results for the production of a $W^+W^-$ pair in
association with a jet at the LHC in QCD at next-to-leading order (NLO). We
include effects of the decay of the massive vector bosons into leptons with
spin correlations and contributions from the third generation of massive
quarks. The calculation is performed using a semi-numerical method for the
virtual corrections, and is implemented in MCFM. In addition to its importance
{\it per se} as a test of the Standard Model, this process is an important
background to searches for the Higgs boson and to many new physics searches. As
an example, we study the impact of NLO corrections to $W^+W^-+$ jet production
on the search for a Higgs boson at the LHC.
