  The framework of relativistic quantum-field theories requires Lorentz
Invariance. Many theories of quantum gravity, on the other hand, include
violations of Lorentz Invariance at small scales and high energies. This
generates a lot of interest in establishing limits on such effects, and, if
possible, observing them directly. Gamma-ray observatories provide a tool to
probe parts of the parameter space of models of Lorentz Invariance Violation
that is not accessible in terrestrial laboratories and man-made accelerators.
Transients, especially gamma-ray bursts, are a particularly promising class of
events to search for such phenomena. By combining cosmological distances with
high energy emission and short duration, emitting photons up to 30 GeV in less
than a second, one can measure the energy dependence of the speed of photons to
one part in $10^{16}$. We will discuss the potential of HAWC to detect effects
of the violation of Lorentz Invariance and place its sensitivity in the context
of existing limits.
