By resonant x-ray scattering at the Mn K edge on La7/8Sr1/8MnO3, we show that an orbital polaron lattice (OPL) develops at the metal-insulator transition of this compound. This orbital reordering explains consistently the unexpected coexistence of ferromagnetic and insulating properties at low temperatures, the quadrupling of the lattice structure parallel to the MnO2 planes, and the observed polarization and azimuthal dependencies. The OPL is a clear manifestation of strong orbital-hole interactions, which play a crucial role for the colossal magnetoresistance effect and the doped manganites in general.