  Using recent polarimetric observations of the Crab Nebula in the hard X-ray
band by INTEGRAL, we show that the absence of vacuum birefringence effects
constrains O(E/M) Lorentz violation in QED to the level |\xi| < 9x10^{-10} at
three sigma CL, tightening by more than three orders of magnitude previous
constraints. We show that planned X-ray polarimeters have the potential the
potential to probe |\xi|~ 10^{-16} by detecting polarization in active galaxies
at red-shift ~1.
