Chiral Bronsted acids (proton donors) have been shown to facilitate a broad range of asymmetric chemical transformations under catalytic conditions without requiring additional toxic or expensive metals(1-8). Although the catalysts developed thus far are remarkably effective at activating polarized functional groups, it is not clear whether organic Bronsted acids can be used to catalyse highly enantioselective transformations of unactivated carbon-carbon multiple bonds. This deficiency persists despite the fact that racemic acid-catalysed 'Markovnikov' additions to alkenes are well known chemical transformations. Here we show that chiral dithiophosphoric acids can catalyse the intramolecular hydroamination and hydroarylation of dienes and allenes to generate heterocyclic products in exceptional yield and enantiomeric excess. We present a mechanistic hypothesis that involves the addition of the acid catalyst to the diene, followed by nucleophilic displacement of the resulting dithiophosphate intermediate; we also report mass spectroscopic and deuterium labelling studies in support of the proposed mechanism. The catalysts and concepts revealed in this study should prove applicable to other asymmetric functionalizations of unsaturated systems.