  We calculate the decay width of the photon splitting into three photons in a
model of quantum electrodynamics with broken Lorentz invariance. We show that
this process can lead to a cut-off in the very-high-energy part of a photon
spectra of astrophysical sources. We obtain the 95\% CL bound on the Lorentz
violating mass scale for photons from the analysis of the very-high-energy part
of the Crab Nebula spectrum, obtained by HEGRA. This bound improves previous
constraints by more than an order of magnitude.
