Various approaches to quantum gravity suggest the possibility of violation of Lorentz symmetry at very high energies. In these cases we expect a modification at low energies of the dispersion relation of photons that contains extra powers of the momentum suppressed by a high energy scale. These terms break boost invariance and can be tested even at relatively low energies. We use the light curves of the very bright short gamma-ray burst GRB 051221A and compare the arrival times of photons at different energies with the expected time delay due to a modified dispersion relation. As no time delay was observed, we set a lower bound of 0.0066 Epl ~ 0.66 × 1017 GeV on the scale of Lorentz invariance violation.