  Compton scattering of quasi-real virtual photons, gamma e+- -> gamma e+-, is
studied with 0.6fb-1 of data collected by the L3 detector at the LEP e+e-
collider at centre-of-mass energies root(s')=189-209GeV. 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 root(s')=
35GeV up to root(s')=175GeV, the highest energy at which Compton scattering was
ever probed. The cross sections of the gamma e+- -> gamma e+- process as a
function of root(s') and of the rest-frame scattering angle are measured,
combined with previous L3 measurements down to root(s')~20GeV, and found to
agree with the QED expectations.
