The unimolecular nucleophilic substitution (S(N)1) mechanism features prominently in every introductory organic chemistry course. In principle, stepwise displacement of a leaving group by a nucleophile via a carbocationic intermediate enables the construction of highly congested carbon centres. However, the intrinsic instability and high reactivity of the carbocationic intermediates make it very difficult to control product distributions and stereoselectivity in reactions that proceed via S(N)1 pathways. Here we report asymmetric catalysis of an S(N)1-type reaction mechanism that results in the enantioselective construction of quaternary stereocentres from racemic precursors. The transformation relies on the synergistic action of a chiral hydrogen-bond-donor catalyst with a strong Lewis-acid promoter to mediate the formation of tertiary carbocationic intermediates at low temperature and to achieve high levels of control over reaction enantioselectivity and product distribution. This work provides a foundation for the enantioconvergent synthesis of other fully substituted carbon stereocentres.