A novel polymer of intrinsic microporosity (PIM) was prepared from a diaminobenzotriptycene monomer using a polymerization reaction based on Tröger's base formation. The polymer (PIM-BTrip-TB) demonstrated an apparent Brunauer, Emmet, and Teller (BET) surface area of 870 m2 g-1, good solubility in chloroform, excellent molecular mass, high inherent viscosity and provided robust thin films for gas permeability measurements. The polymer is highly permeable (e.g., PH2 = 9980; PO2 = 3290 Barrer) with moderate selectivity (e.g., PH2/PN2 = 11.0; PO2/PN2 = 3.6) so that its data lie over the 2008 Robeson upper bounds for the H2/N2, O2/N2, and H2/CH4 gas pairs and on the upper bound for CO2/CH4. On aging, the polymer demonstrates a drop in permeability, which is typical for ultrapermeable polymers, but with a significant increase in gas selectivities (e.g., PO2 = 1170 Barrer; PO2/PN2 = 5.4).