  Several models of Quantum Gravity predict Lorentz Symmetry breaking at energy
scales approaching the Planck scale (10^{19} GeV). With present photon data
from the observations of distant astrophysical sources, it is possible to
constrain the Lorentz Symmetry breaking linear term in the standard photon
dispersion relations. Gamma-ray Bursts (GRB) and flaring Active Galactic Nuclei
(AGN) are complementary to each other for this purpose, since they are observed
at different distances in different energy ranges and with different levels of
variability. Following a previous publication of the High Energy Stereoscopic
System (H.E.S.S.) collaboration, a more sensitive event-by-event method
consisting of a likelihood fit is applied to PKS 2155-304 flare data of MJD
53944 (July 28, 2006) as used in the previous publication. The previous limit
on the linear term is improved by a factor of ~3 up to M^{l}_{QG} > 2.1x10^{18}
GeV and is currently the best result obtained with blazars. The sensitivity to
the quadratic term is lower and provides a limit of M^{q}_{QG} > 6.4x10^10 GeV,
which is the best value obtained so far with an AGN and similar to the best
limits obtained with GRB.
