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 αs(M2Z) = 0.1240 ± 0.0008 (stat) ± 0.0010 (exp) ± 0.0011 (had) ± 0.0029 (theo).