The adsorption of a monolayer of methane upon the (100) surface of MgO was studied using a first-principles-based density functional approach employing a plane-wave basis set and periodic boundary conditions. Adsorption at both magnesium and oxygen sites was investigated, as were methane orientations where one, two, or three hydrogen atoms point toward the surface plane. In addition, the effect of one methane molecule on its neighbors was investigated by considering arrangements where translational symmetry across the surface was accompanied by appropriate rotations of the methane molecule. The minimum-energy configuration has the methane molecules located directly above a surface magnesium atom, the principal axis of the ${C}_{2v}$ molecule is normal to the surface plane, and pairs of hydrogen atoms are oriented along the lattice lines that include adjacent (surface) oxygen atoms. Furthermore, neighboring methane molecules are rotated by 90\ifmmode^\circ\else\textdegree\fi{} to reduce the H-H steric interactions. This arrangement has direct ramifications for the stability of other proposed, similar arrangements.