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Recent analysis of satellite data obtained during the 9 October 2012 geomagnetic storm identified the development of peaks in electron phase space density, which are compelling evidence for local electron acceleration in the heart of the outer radiation belt, but are inconsistent with acceleration by inward radial diffusive transport. However, the precise physical mechanism responsible for the acceleration on 9 October was not identified. Previous modelling has indicated that a magnetospheric electromagnetic emission known as chorus could be a potential candidate for local electron acceleration, but a definitive resolution of the importance of chorus for radiation-belt acceleration was not possible because of limitations in the energy range and resolution of previous electron observations and the lack of a dynamic global wave model. Here we report high-resolution electron observations obtained during the 9 October storm and demonstrate, using a two-dimensional simulation performed with a recently developed time-varying data-driven model, that chorus scattering explains the temporal evolution of both the energy and angular distribution of the observed relativistic electron flux increase. Our detailed modelling demonstrates the remarkable efficiency of wave acceleration in the Earth's outer radiation belt, and the results presented have potential application to Jupiter, Saturn and other magnetized astrophysical objects.