Carbocations can be categorized into classical carbenium ions and non-classical carbonium ions. These intermediates are ubiquitous in reactions of both fundamental and practical relevance, finding application in the petroleum industry as well as the discovery of new drugs and materials. Conveying stereochemical information to carbocations is therefore of interest to a range of chemical fields. While previous studies targeted systems proceeding through classical ions, enantiocontrol over their non-classical counterparts has remained unprecedented. Here we show that strong and confined chiral acids catalyse enantioselective reactions via the non-classical 2-norbornyl cation. This reactive intermediate is generated from structurally different precursors by leveraging the reactivity of various functional groups to ultimately deliver the same enantioenriched product. Our work demonstrates that tailored catalysts can act as suitable hosts for simple, non-functionalized carbocations via a network of non-covalent interactions. We anticipate that the methods described herein will provide catalytic accessibility to valuable carbocation systems.