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Chiral amines can be made by insertion of a carbene into an N–H bond using two-catalyst systems that combine a transition metal-based carbene-transfer catalyst and a chiral proton-transfer catalyst to enforce stereocontrol. Haem proteins can effect carbene N–H insertion, but asymmetric protonation in an active site replete with proton sources is challenging. Here we describe engineered cytochrome P450 enzymes that catalyse carbene N–H insertion to prepare biologically relevant α-amino lactones with high activity and enantioselectivity (up to 32,100 total turnovers, >99% yield and 98% e.e.). These enzymes serve as dual-function catalysts, inducing carbene transfer and promoting the subsequent proton transfer with excellent stereoselectivity in a single active site. Computational studies uncover the detailed mechanism of this new-to-nature enzymatic reaction and explain how active-site residues accelerate this transformation and provide stereocontrol.