The class of coordination polymers known as metal-organic frameworks (MOFs) has three-dimensional porous structures that are considered as a promising alternative to zeolites and other nanoporous materials for catalysis, gas adsorption, and gas separation applications. In this paper, we present the first study of gas diffusion inside an MOF and compare the observed diffusion to known behaviors in zeolites. Using grand canonical Monte Carlo and equilibrium molecular dynamics, we calculate the adsorption isotherm and self-, corrected, and transport diffusivities for argon in the CuBTC metal-organic framework. Our results indicate that diffusion of Ar in CuBTC is very similar to Ar diffusion in silica zeolites in magnitude, concentration, and temperature dependence. This conclusion appears to apply to a broad range of MOF structures.