We report on the electrostatic modulation of superconductivity in very thin films of cuprate superconductors using a field-effect device based on a SrTiO3 single-crystal gate insulator. A T-c modulation of 3.5 K and a 37% change of the normal state resistance have been observed in an epitaxial bilayer composed of an insulating PrBa2Cu3O7-delta layer deposited on top of a superconducting NdBa2Cu3O7-delta film, two unit cells thick. To achieve large electric fields, the thickness of the commercial dielectric single-crystal SrTiO3 substrate (also used as the gate insulator) was reduced to 110 mum. The dielectric properties of the gate insulator were characterized as a function of temperature and electric field and the magnitude of the field effect was quantified. A T-c enhancement of 2.8 K was obtained for an applied field of -1.8x10(6) V/m, corresponding to a polarization of -4 muC/cm(2).