Covalent organic frameworks (COFs) have emerged as a novel platform for material design and functional explorations, but it remains a challenge to synthetically functionalize targeted structures for task-specific applications. Optically pure 1,1'-bi-2-naphthol (BINOL) is one of the most important sources of chirality for organic synthesis and materials science, but it has not yet been used in construction of COFs for enantioselective processes. Here, by elaborately designing and choosing an enantiopure BINOL-based linear dialdehyde and a tris(4-aminophenyl)benzene derivative or tetrakis(4-aminophenyl)ethene as building blocks, two imine-linked chiral fluorescent COFs with a 2D layered hexagonal or tetragonal structure are prepared. The COF containing flexible tetraphenylethylene units can be readily exfoliated into ultrathin 2D nanosheets and electrospun to make free-standing nanofiber membrane. In both the solution and membrane systems, the fluorescence of COF nanosheets can be effectively quenched by chiral odor vapors via supramolecular interactions with the immobilized BINOL moieties, leading to remarkable chiral vapor sensors. Compared to the BINOL-based homogeneous and membrane systems, the COF nanosheets exhibited greatly enhanced sensitivity and enantioselectivity owing to the confinement effect and the conformational rigidity of the sensing BINOL groups in the framework. The ability to place such a useful BINOL chiral auxiliary inside open channels of COFs capable of amplifying chiral discrimination of the analytes represents a major step toward the rational synthesis of porous molecular materials for more chirality applications.