  We present a measurement of the strong coupling alpha_S using data collected
with the JADE detector at centre-of-mass energies between 14 and 44 GeV. The
three-jet rate as a function of the transition parameter ycut is determined
using the Durham jet algorithm and the distribution is compared to QCD
predictions. Recent theoretical calculations predict the three-jet rate at
next-to-next-to-leading order. For the first time a measurement of alpha_S is
presented using QCD predictions at next-to-next-to-leading order matched to
predictions at next-to-leading logarithmic approximation, with subleading terms
being included as well. We obtain
alpha_S(Mz)=0.1199+-0.0010(stat.)+-0.0021(exp.)+-0.0054(had.)+-0.0007(theo.)
being consistent with the world average value of alpha_S.
