To impact carbon emissions, new materials for carbon capture must be inexpensive, robust, and able to adsorb CO2 specifically streams produced by using fossil fuels to generate electricity. We show, from a mixture of other gases. In particular, materials must be tolerant to the water vapor and to the acidic impurities that are present in gas that a porous organic polymer has excellent CO2 capacity and high CO2 selectivity under conditions relevant to precombustion CO2 capture. Unlike polar adsorbents, such as zeolite 13x and the metal-organic framework, HKUST-1, the CO2 adsorption capacity for the hydrophobic polymer is hardly affected by the adsorption of water vapor. The polymer is even stable to boiling in concentrated acid for extended periods, a property that is matched by few microporous adsorbents. The polymer adsorbs CO2 in a different way from rigid materials by physical swelling, much as a sponge adsorbs water. This gives rise to a higher CO2 capacities and much better CO2 selectivity than for other water-tolerant, nonswellable frameworks, such as activated carbon and ZIF-8. The polymer has superior function as a selective gas adsorbent, even though its constituent monomers are very simple organic feedstocks, as would be required for materials preparation on the large industrial scales required for carbon capture.