We present a measurement of the strong coupling α S using the three-jet rate measured with the Durham algorithm in e+e− -annihilation using data of the JADE experiment at centre-of-mass energies between 14 and 44 GeV. Recent theoretical improvements provide predictions of the three-jet rate in e+e− -annihilation at next-to-next-to-leading order. In this paper a measurement of the three-jet rate is used to determine the strong coupling α S from a comparison to next-to-next-to-leading order predictions matched with next-to-leading logarithmic approximations and yields a value for the strong coupling consistent with the world average.