Amines with remote stereocentres (stereocentres that are three or more bonds away from the C–N bond) are important structural elements in many pharmaceutical agents and natural products. However, previously reported methods to prepare these compounds in an enantioselective manner are indirect and require multistep synthesis. Here, we report a copper-hydride-catalysed, enantioselective synthesis of γ- or δ-chiral amines from readily available allylic alcohols, esters and ethers using a reductive relay hydroamination strategy (a net reductive process in which an amino group is installed at a site remote from the original carbon–carbon double bond). The protocol was suitable for substrates containing a wide range of functional groups and provided remote chiral amine products with high levels of regio- and enantioselectivity. Sequential amination of substrates containing several carbon–carbon double bonds could be achieved, demonstrating the high chemoselectivity of this process.