A synthetic method for obtaining enantiopure and twisted baskets of type (P)-3 is described. These chiral cavitands were found to fold quinoline gates, at the rim of their twisted platform, in acetonitrile and give molecular capsules that assemble into large unilamellar vesicles. In a less polar dichloromethane, however, cup-shaped (P)-3 packed into vesicles but with the quinoline gates in an unfolded orientation. The ability of twisted baskets to form functional nanostructured materials could be of interest for building stereoselective sensors and catalysts.