A lifetime measurement of the 19/2− state in 207Pb has been performed using the Recoil Distance Doppler-Shift (RDDS) method. The nuclei of interest were produced in multi-nucleon transfer reactions induced by a 208Pb beam impinging on a 100Mo enriched target. The beam-like nuclei were detected and identified in terms of their atomic mass number in the VAMOS++ spectrometer while the prompt γ rays were detected by the AGATA tracking array. The measured large reduced transition probability B(E3,19/2−→13/2+)=40(8) W.u. is the first indication of the octupole phonon at high spin in 207Pb. An analysis in terms of a particle-octupole-vibration coupling model indicates that the measured B(E3) value in 207Pb is compatible with the contributions from single-phonon and single particle E3 as well as E3 strength arising from the double-octupole-phonon 6+ state, all adding coherently. A crucial aspect of the coupling model, namely the strong mixing between single-hole and the phonon-hole states, is confirmed in a realistic shell-model calculation.