Metal organic frameworks are among the most promising materials for industrial gas separations, including the removal of carbon dioxide from natural gas, although substantial improvements in adsorption selectivity are still sought. Herein, we use equilibrium adsorption experiments to demonstrate that the flexible metal organic framework Co(bdp) (bdp(2-) = 1,4-benzenedipyrazolate) exhibits a large CO2 adsorption capacity and approaches complete exclusion of CH4 under 50:50 mixtures of the two gases, leading to outstanding CO2/CH4 selectivity under these conditions. In situ powder X-ray diffraction data indicate that this selectivity arises from reversible guest templating, in which the framework expands to form a CO2 clathrate and then collapses to the nontemplated phase upon desorption. Under an atmosphere dominated by CH4, Co(bdp) adsorbs minor amounts of CH4 along with CO2, highlighting the importance of studying all relevant pressure and composition ranges via multicomponent measurements when examining mixed-gas selectivity in structurally flexible materials. Altogether, these results show that Co(bdp) may be a promising CO2/CH4 separation material and provide insights for the further study of flexible adsorbents for gas separations.