Organic solvent nanofiltration (OSN) membranes with ultrathin separation layers down to 35 nm in thickness fabricated from a polymer of intrinsic microporosity (PIM-1) are presented. These membranes exhibit exceptionally fast permeation of n-heptane with a rejection for hexaphenylbenzene of about 90%. A 35 nm thick PIM-1 membrane possesses a Young's modulus of 222 MPa, and shows excellent stability under hydraulic pressures of up to 15 bar in OSN. A maximum permeance for n-heptane of 18 Lm(-2)h(-1) bar(-1) is achieved with a 140 nm thick membrane, which is about two orders of magnitude higher than Starmem240 (a commercial polyimide-based OSN membrane). Unexpectedly, decreasing the film thickness below 140 nm results in an anomalous decrease in permeance, which appears to be related to a packing enhancement of PIM-1, as measured by light interferometry. Further, thermal annealing of the membranes formed from PIM-1 reveals that their permeance is preserved up to temperatures in excess of 150 degrees C, whereas the permeance of conventional, integrally skinned, asymmetric polyimide OSN membranes decreases significantly when they are annealed under the same conditions. To rationalize this key difference in response of functional performance to annealing, the concept of membranes with intrinsic microporosity (MIMs) versus membranes with extrinsic microporosity (MEMs) is introduced.