  We present the first determination of the strong coupling constant from the
three-jet rate in e+e- annihilation at LEP, based on a next-to-next-to-leading
order (NNLO) perturbative QCD prediction. More precisely, we extract alpha_s by
fitting perturbative QCD predictions at O(alpha_s^3) to data from the ALEPH
experiment at LEP. Over a large range of the jet-resolution parameter ycut this
observable is characterised by small non-perturbative corrections and an
excellent stability under renormalisation scale variation. For the three-jet
rate at ln(ycut) = -3.9 we find alpha_s(MZ) = 0.1175 +/- 0.0020(exp) \+/-
0.0015(theo), which is among the most precise determinations from jet
observables at LEP.
