  We compute the total cross section as well as angular and energy
distributions for process $e^+e^-\to\gamma\gamma\gamma$ with both unpolarized
and polarized beams in the framework of noncommutative quantum electrodynamics
(NCQED). The calculation is performed in the center of mass of colliding
electron and positron and is evaluated for energies and integrated luminosities
appropriate to future linear colliders. We find that by using unpolarized beams
it is possible to probe the Lorentz symmetry violating azimuthal dependence of
the cross section. Furthermore, with polarized beams the left-right asymmetry
of the CP violating NCQED amplitudes can be used to obtain bounds on the
noncommutative scale $\Lambda_{NC}$ which exceed 1.0 TeV.
