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The nitrogen-vacancy (NV) centre in diamond is a promising candidate for a solid-state qubit. However, its charge state is known to be unstable, discharging from the qubit state NV(-) into the neutral state NV(0) under various circumstances. Here we demonstrate that the charge state can be controlled by an electrolytic gate electrode. This way, single centres can be switched from an unknown non-fluorescent state into the neutral charge state NV(0), and the population of an ensemble of centres can be shifted from NV(0) to NV(-). Numerical simulations confirm the manipulation of the charge state to be induced by the gate-controlled shift of the Fermi level at the diamond surface. This result opens the way to a dynamic control of transitions between charge states and to explore hitherto inaccessible states, such as NV(+).