  We analyze the timing of photons observed by the MAGIC telescope during a
flare of the active galactic nucleus Mkn 501 for a possible correlation with
energy, as suggested by some models of quantum gravity (QG), which predict a
vacuum refractive index \simeq 1 + (E/M_{QGn})^n, n = 1,2. Parametrizing the
delay between gamma-rays of different energies as \Delta t =\pm\tau_l E or
\Delta t =\pm\tau_q E^2, we find \tau_l=(0.030\pm0.012) s/GeV at the 2.5-sigma
level, and \tau_q=(3.71\pm2.57)x10^{-6} s/GeV^2, respectively. We use these
results to establish lower limits M_{QG1} > 0.21x10^{18} GeV and M_{QG2} >
0.26x10^{11} GeV at the 95% C.L. Monte Carlo studies confirm the MAGIC
sensitivity to propagation effects at these levels. Thermal plasma effects in
the source are negligible, but we cannot exclude the importance of some other
source effect.
