Compton scattering of quasi-real virtual photons, γe^± → γe^±, is studied with 0.6 fb⁻¹ of data collected by the L3 detector at the LEP e⁺e⁻ collider at centre-of-mass energies √s = 189–209 GeV. About 4500 events produced by the interaction of virtual photons emitted by e^± of one beam with e^∓ of the opposite beam are collected for effective centre-of-mass energies of the photon–electron and photon–positron systems in the range from √s' = 35 GeV up to √s' = 175 GeV, the highest energy at which Compton scattering was ever probed. The cross sections of the γe^± → γe^± process as a function of √s' and of the rest-frame scattering angle are measured, combined with previous L3 measurements down to √s'≃20 GeV, and found to agree with the QED expectations.Facultad de Ciencias Exactas