Two-dimensional (2D) metal-organic frameworks (MOFs) have received a great deal of attention due to their relatively high charge carrier mobility and low resistivity. Here we report on the temperature-dependent charge transport properties of a 2D cobalt 2,3,6,7,10,11-triphenylenehexathiolate framework. Variable temperature resistivity studies reveal a transition from a semiconducting to a metallic phase with decreasing temperature, which is unprecedented in MOFs. We find this transition to be highly dependent on the film thickness and the amount of solvent trapped in the pores, with density functional theory calculations of the electronic-structure supporting the complex metallic conductivity of the material. These results identify the first experimentally observed MOF that exhibits band-like metallic conductivity.