In this talk I report on the status of the calculation of the next-to-leading order (NLO) QCD corrections to top-quark pair production together with a jet in hadronic collisions. A precise understanding of this process is of great importance, because pp \to t \bar t  + 1 jet is an important background for the Higgs search in the Higgs mass range 120--180 GeV. In addition the reaction is also an interesting process for precise measurements in the top sector.

PACS numbers: 12.38.Bx, 12.38.--t, 14.65.Ha