We report a measurement of the strong coupling constant, alpha(s)(M-Z), extracted from inclusive jet production in p (p) over bar collisions at root(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. The value of as 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 +/- 0.0001(stat)(-0.0095)(+0.0081)(expt. syst). The associated theoretical uncertainties are mainly due to the choice of renormalization scale ((+6%)(-4%)) and input parton distribution functions (5%).