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 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).

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