The polar corundum structure type offers a route to new room temperature multiferroic materials, as the partial LiNbO3-type cation ordering that breaks inversion symmetry may be combined with long-range magnetic ordering of high spin d5 cations above room temperature in the AFeO3 system. We report the synthesis of a polar corundum GaFeO3 by a high-pressure, high-temperature route and demonstrate that its polarity arises from partial LiNbO3-type cation ordering by complementary use of neutron, X-ray, and electron diffraction methods. In situ neutron diffraction shows that the polar corundum forms directly from AlFeO3-type GaFeO3 under the synthesis conditions. The A3+/Fe3+ cations are shown to be more ordered in polar corundum GaFeO3 than in isostructural ScFeO3. This is explained by DFT calculations which indicate that the extent of ordering is dependent on the configurational entropy available to each system at the very different synthesis temperatures required to form their corundum structures. Polar corundum GaFeO3 exhibits weak ferromagnetism at room temperature that arises from its Fe2O3-like magnetic ordering, which persists to a temperature of 408 K. We demonstrate that the polarity and magnetization are coupled in this system with a measured linear magnetoelectric coupling coefficient of 0.057 ps/m. Such coupling is a prerequisite for potential applications of polar corundum materials in multiferroic/magnetoelectric devices. (Graph Presented).