The synthesis of molecular-sieving zeolitic membranes by the assembly of building blocks, avoiding the hydrothermal treatment, is highly desired to improve reproducibility and scalability. Here we report exfoliation of the sodalite precursor RUB-15 into crystalline 0.8-nm-thick nanosheets, that host hydrogen-sieving six-membered rings (6-MRs) of SiO4 tetrahedra. Thin films, fabricated by the filtration of a suspension of exfoliated nanosheets, possess two transport pathways: 6-MR apertures and intersheet gaps. The latter were found to dominate the gas transport and yielded a molecular cutoff of 3.6 Å with a H2/N2 selectivity above 20. The gaps were successfully removed by the condensation of the terminal silanol groups of RUB-15 to yield H2/CO2 selectivities up to 100. The high selectivity was exclusively from the transport across 6-MR, which was confirmed by a good agreement between the experimentally determined apparent activation energy of H2 and that computed by ab initio calculations. The scalable fabrication and the attractive sieving performance at 250-300 °C make these membranes promising for precombustion carbon capture.