Efficient catalytic reactions that can generate C-C bonds enantioselectively, and ones that can produce trisubstituted alkenes diastereoselectively, are central to research in organic chemistry. Transformations that accomplish these two tasks simultaneously are in high demand, particularly if the catalysts, substrates and reagents are inexpensive and if the reaction conditions are mild. Here we report a facile multicomponent catalytic process that begins with a chemoselective, site-selective and diastereoselective copper-boron addition to a monosubstituted allene; the resulting boron-substituted organocopper intermediates then participate in a similarly selective allylic substitution. The products, which contain a stereogenic carbon centre, a monosubstituted alkene and an easily functionalizable Z-trisubstituted alkenylboron group, are obtained in up to 89 per cent yield, with more than 98 per cent branch-selectivity and stereoselectivity and an enantiomeric ratio greater than 99:1. The copper-based catalyst is derived from a robust heterocyclic salt that can be prepared in multigram quantities from inexpensive starting materials and without costly purification procedures. The utility of the approach is demonstrated through enantioselective synthesis of gram quantities of two natural products, namely rottnestol and herboxidiene (also known as GEX1A).