Increases in the gate capacitance of field-effect transistor structures allow the production of lower-power devices that are compatible with higher clock rates, driving the race for developing high-k dielectrics. However, many-body effects in an electronic system can also enhance capacitance. Onto the electron system that forms at the LaAlO3/SrTiO3 interface, we fabricated top-gate electrodes that can fully deplete the interface of all mobile electrons. Near depletion, we found a greater than 40% enhancement of the gate capacitance. Using an electric-field penetration measurement method, we show that this capacitance originates from a negative compressibility of the interface electron system. Capacitance enhancement exists at room temperature and arises at low electron densities, in which disorder is strong and the in-plane conductance is much smaller than the quantum conductance.