Recent developments in the technology of van der Waals heterostructures1, 2 made from two-dimensional atomic crystals3, 4 have already led to the observation of new physical phenomena, such as the metal–insulator transition5 and Coulomb drag6, and to the realization of functional devices, such as tunnel diodes7, 8, tunnel transistors9, 10 and photovoltaic sensors11. An unprecedented degree of control of the electronic properties is available not only by means of the selection of materials in the stack12, but also through the additional fine-tuning achievable by adjusting the built-in strain and relative orientation of the component layers13, 14, 15, 16, 17. Here we demonstrate how careful alignment of the crystallographic orientation of two graphene electrodes separated by a layer of hexagonal boron nitride in a transistor device can achieve resonant tunnelling with conservation of electron energy, momentum and, potentially, chirality. We show how the resonance peak and negative differential conductance in the device characteristics induce a tunable radiofrequency oscillatory current that has potential for future high-frequency technology.