Nanocrystal quantum dots have favourable light-emitting properties. They show photoluminescence with high quantum yields, and their emission colours depend on the nanocrystal size—owing to the quantum-confinement effect—and are therefore tunable. However, nanocrystals are difficult to use in optical amplification and lasing. Because of an almost exact balance between absorption and stimulated emission in nanoparticles excited with single electron–hole pairs (excitons), optical gain can only occur in nanocrystals that contain at least two excitons. A complication associated with this multiexcitonic nature of light amplification is fast optical-gain decay induced by non-radiative Auger recombination, a process in which one exciton recombines by transferring its energy to another. Here we demonstrate a practical approach for obtaining optical gain in the single-exciton regime that eliminates the problem of Auger decay. Specifically, we develop core/shell hetero-nanocrystals engineered in such a way as to spatially separate electrons and holes between the core and the shell (type-II heterostructures). The resulting imbalance between negative and positive charges produces a strong local electric field, which induces a giant (100 meV or greater) transient Stark shift of the absorption spectrum with respect to the luminescence line of singly excited nanocrystals. This effect breaks the exact balance between absorption and stimulated emission, and allows us to demonstrate optical amplification due to single excitons.