QCD corrections to associated<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mi>¯</mml:mi></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>h</mml:mi></mml:math>production at the Fermilab Tevatron

We present in detail the calculation of the $\mathcal{O}({\ensuremath{\alpha}}_{s}^{3})$ inclusive total cross section for the process $p\overline{p}\ensuremath{\rightarrow}t\overline{t}h$ in the Standard Model, at the Fermilab Tevatron center-of-mass energy $\sqrt{{s}_{H}}=2\mathrm{TeV}.$ The next-to-leading order QCD corrections significantly reduce the renormalization and factorization scale dependence of the Born cross section. They slightly decrease or increase the Born cross section depending on the values of the renormalization and factorization scales.