Compton scattering of quasi-real virtual photons, γe±→γe±γe±→γe±, is studied with 0.6 fb−1 of data collected by the L3 detector at the LEP e+e−e+e− collider at centre-of-mass energies √s=189-209 GeVs=189–209 GeV. About 4500 events produced by the interaction of virtual photons emitted by e±e± of one beam with e∓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±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