  We determine the strong coupling constant alphas and its energy dependence
from the pT dependence of the inclusive jet cross section in ppbar collisions
at sqrt(s)=1.96 TeV. The strong coupling constant is determined over the
transverse momentum range 50 < pT < 145 GeV. Using perturbative QCD
calculations to order O(alphas^3) combined with O(alphas^4) contributions from
threshold corrections, we obtain alphas(MZ) = 0.1161 +0.0041 -0.0048. This is
the most precise result obtained at a hadron-hadron collider.
