The development of a general catalytic method for the direct and stereoselective construction of contiguous all-carbon quaternary stereocentres remains a formidable challenge in chemical synthesis. Here, we report a highly enantio- and diastereoselective [3+2] annulation reaction of 5-vinyloxazolidinones and activated trisubstituted alkenes catalysed by a palladium complex bearing a newly devised phosphine ligand with a chiral ammonium salt component, which enables the single-step construction of three contiguous stereocentres, including vicinal all-carbon quaternary stereocentres, in a five-membered heterocyclic framework. This stereoselective cycloaddition protocol relies on the remarkable ability of the chiral ligand to rigorously control the absolute stereochemistry of each chiral centre associated with the multiple bond-forming events, and provides a reliable catalytic process for the asymmetric synthesis of densely functionalized pyrrolidines.