Event Shape Data from e+e− annihilation into hadrons collected by the JADE experiment at centre-of-mass energies between 14 GeV and 44 GeV are used to determine the strong coupling αS. QCD predictions complete to next-to-next-to-leading order (NNLO), alternatively combined with resummed next-to-leading-log-approximation (NNLO + NLLA) calculations, are used. The combined value from six different event shape observables at the six JADE centre-of-mass energies using the NNLO calculations is \ensuremath\ensuremathαS(\ensuremathm\ensuremathZ0)=0.1210±0.0007\ensuremath(stat.)±0.0021\ensuremath(exp.)±0.0044\ensuremath(had.)±0.0036\ensuremath(theo.) and with the NNLO + NLLA calculations the combined value is \ensuremath\ensuremathαS(\ensuremathm\ensuremathZ0)=0.1172±0.0006\ensuremath(stat.)±0.0020\ensuremath(exp.)±0.0035\ensuremath(had.)±0.0030\ensuremath(theo.). The stability of the NNLO and NNLO + NLLA results with respect to missing higher order contributions, studied by variations of the renormalisation scale, is improved compared to previous results obtained with NLO + NLLA or with NLO predictions only. The observed energy dependence of αS agrees with the QCD prediction of asymptotic freedom and excludes absence of running with 99% confidence level.