Utilizing single-crystal synchrotron x-ray scattering, we observe distorted CuO2 planes in the electron-doped superconductor Pr1−xLaCexCuO4+δ, x = 0.12. Resolution-limited rods of scattering are indicative of a long-range two-dimensional 22√×22√ superstructure in the a−b plane, adhering to planar space-group symmetry p4gm, which is subject to stacking disorder perpendicular to the planes. This superstructure is present only in annealed, superconducting samples, but not in the as-grown, nonsuperconducting samples. These long-range distortions of the CuO2 planes, which are generally considered to be detrimental to superconductivity, have avoided detection to date due to the challenges of observing and interpreting subtle diffuse-scattering features.