We exploit recent polarimetric observations of the Crab Nebula in the hard X-ray band by IN- TEGRAL to show that the absence of vacuum birefringence effects constrains O(E/M) Lorentz violation in QED to the level |ξ | < 9 × 10^{−10} (at 3σ CL). This tightens by more than three or- ders of magnitude previous constraints. We also show that planned X-ray polarimeters have the potential to probe |ξ | ∼ 10^{−16} by detecting polarization in active galaxies at red-shift ∼ 1.
