A hybrid method that combines density functional theory for periodic structures with wave function-based electron correlation methods for finite-size models of adsorption sites is employed to calculate energies for adsorption of CH4 onto different sites in the metal-organic framework (MOF) CPO-27-Mg (Mg-MOF-74) with chemical accuracy. The adsorption energies for the Mg2+, linker, second layer sites are -27.8, -18.3, and -15.1 kJ/mol. Adsorbate-adsorbate interactions increase the average CH4 adsorption energy by about 10% (2.4 kJ/mol). The free rotor-harmonic oscillator-ideal gas model is applied to calculate free energies/equilibrium constants for adsorption on the individual sites. This information is used in a multisite Langmuir model, augmented with a Bragg-Williams model for lateral interactions, to calculate adsorption isotherms. This ab initio approach yields the contributions of the individual sites to the final isotherms and also of the lateral interactions that contribute about 15% to the maximum excess adsorption capacity. Isotherms are calculated for both absolute amounts, for calculation of isosteric heats of adsorption as function of coverage, and excess amounts, for comparison with measured isotherms. Agreement with observed excess isotherms is reached if the experimentally determined limited accessibility of adsorption sites (78%) is taken into account