The application of an electric field through two-dimensional materials (2DMs) modifies their properties. For example, a bandgap opens in semimetallic bilayer graphene while the bandgap shrinks in few-layer 2D semiconductors. The maximum electric field strength achievable in conventional devices is limited to ≤0.3 V/nm by the dielectric breakdown of gate dielectrics. Here, we overcome this limit by suspending a 2DM between two volumes of ionic liquid (IL) with independently controlled potentials. The potential difference between the ILs falls across an ultrathin layer consisting of the 2DM and the electrical double layers above and below it, producing an intense electric field larger than 4 V/nm. This field is strong enough to close the bandgap of few-layer WSe2, thereby driving a semiconductor-to-metal transition. The ability to apply fields an order of magnitude higher than what is possible in dielectric-gated devices grants access to previously-inaccessible phenomena occurring in intense electric fields.