  We report a measurement of the strong coupling constant, $\alpha_s(M_Z)$,
extracted from inclusive jet production in $p\bar{p}$ collisions at
$\sqrt{s}=$1800 GeV. The QCD prediction for the evolution of $\alpha_s$ with
jet transverse energy $E_T$ is tested over the range 40<$E_T$<450 GeV using
$E_T$ for the renormalization scale. The data show good agreement with QCD in
the region below 250 GeV. In the text we discuss the data-theory comparison in
the region from 250 to 450 GeV. The value of $\alpha_s$ at the mass of the
$Z^0$ boson averaged over the range 40<$E_T$<250 GeV is found to be
$\alpha_s(M_{Z})= 0.1178 \pm 0.0001{(\rm stat)}^{+0.0081}_{-0.0095}{\rm (exp.
syst)}$. The associated theoretical uncertainties are mainly due to the choice
of renormalization scale ($^{+6%}_{-4%}$) and input parton distribution
functions (5%).
