We discuss the production of top–anti-top quark pairs in association with a hard jet at the Tevatron and at the LHC and we report on the calculation of the next-to-leading order QCD corrections to this process. Numerical results for the top–anti-top+jet cross section and the forward–backward charge asymmetry are presented. The corrections stabilize the leading-order prediction for the cross section. In contrast, the charge asymmetry receives large corrections. The dependence of the cross section as well as the asymmetry on the minimum transverse momenta used to define the additional jet is studied in detail for the Tevatron.
