  We present the first determination of the strong coupling constant from a fit
of next-to-next-to-leading order QCD predictions to event-shape variables,
measured in $e^+e^-$ annihilations at LEP. The data have been collected by the
ALEPH detector at centre-of-mass energies between 91 and 206 GeV. Compared to
results of next-to-leading order fits we observe that the central fit values
are lower by about 10%, with considerably reduced scatter among the results
obtained with different event-shape variables. The dominant systematic
uncertainty from renormalization scale variations is reduced by a factor of
two. By combining the results for several event-shape variables and
centre-of-mass energies, we find \alpha_s(M_Z^2) =
0.1240+-0.0008(stat)+-0.0010(exp)+-0.0011(had)+-0.0029(theo).
