  We present the calculation of the cross section for Higgs boson production in
association with a top quark pair plus one jet, at next-to-leading-order (NLO)
accuracy in QCD. All mass dependence is retained without recurring to any
approximation. After including the complete NLO QCD corrections, we observe a
strong reduction in the scale dependence of the result. We also show
distributions for the invariant mass of the top quark pair, with and without
the additional jet, and for the transverse momentum and the pseudorapidity of
the Higgs boson. Results for the virtual contributions are obtained with a
novel reduction approach based on integrand decomposition via Laurent
expansion, as implemented in the library Ninja. Cross sections and differential
distributions are obtained with an automated setup which combines the GoSam and
Sherpa frameworks.
