Membranes based on a porous two-dimensional selective layer offer the potential to achieve exceptional performance to improve energy efficiency and reduce the cost for carbon capture. So far, separation from two-dimensional pores has exploited differences in molecular mass or size. However, competitive sorption of CO2 with the potential to yield high permeance and selectivity has remained elusive. Here we show that a simple exposure of ammonia to oxidized single-layer graphene at room temperature incorporates pyridinic nitrogen at the pore edges. This leads to a highly competitive but quantitatively reversible binding of CO2 with the pore. An attractive combination of CO2/N2 separation factor (average of 53) and CO2 permeance (average of 10,420) from a stream containing 20 vol% CO2 is obtained. Separation factors above 1,000 are achieved for dilute (~1 vol%) CO2 stream, making the membrane promising for carbon capture from diverse point emission sources. Thanks to the uniform and scalable chemistry, high-performance centimetre-scale membranes are demonstrated. The scalable preparation of high-performance two-dimensional membranes opens new directions in membrane science.