The possibility of anisotropies in the speed of light relative to the limiting speed of electrons is considered. The absence of sidereal variations in the energy of Compton-edge photons at the European Synchrotron Radiation Facility's GRAAL facility constrains such anisotropies representing the first nonthreshold collision-kinematics study of Lorentz violation. When interpreted within the minimal standard-model extension, this result yields the two-sided limit of 1.6×10(-14) at 95% confidence level on a combination of the parity-violating photon and electron coefficients (κ(o+))(YZ), (κ(o+))(ZX), c(TX), and c(TY). This new constraint provides an improvement over previous bounds by 1 order of magnitude.