Amine-based absorbents play a central role in CO2 sequestration and utilization. Amines react selectively with CO2, but a drawback is the unproductive weight of solvent or support in the absorbent. Efforts have focused on metal organic frameworks (MOFs) reaching extremely high CO2 capacity, but limited selectivity to N2 and CH4, and decreased uptake at higher temperatures. A desirable system would have selectivity (cf. amine) and high capacity (cf. MOF), but also increased adsorption at higher temperatures. Here, we demonstrate a proof-of-concept where polyethyleneimine (PEI) is converted to a high capacity and highly selective CO2 absorbent using buckminsterfullerene (C60) as a cross-linker. PEI-C60 (CO2 absorption of 0.14 g/g at 0.1 bar/90°C) is compared to one of the best MOFs, Mg-MOF-74 (0.06 g/g at 0.1 bar/90°C), and does not absorb any measurable amount of CH4 at 50 bar. Thus, PEI-C60 can perform better than MOFs in the sweetening of natural gas.