We have fabricated nanometer-spaced electrodes on electron-transparent silicon nitride membranes. A thin Cr/Au layer is evaporated on the backside of the membrane which serves as a gate electrode. Using these devices, we have performed three-terminal electron transport measurements on gold nano-particles at liquid helium temperature. Coulomb Blockade features have been observed and the capacitance to the gate has been extracted. After transport measurements, the Cr/Au back gate is removed and the devices are inspected with a transmission-electron microscope (TEM). TEM inspection reveals the presence of a few nano-particles in the nanogap, which is in agreement with the transport measurements. In addition, the nano-particle size as observed by TEM coincides with the one estimated from the gate capacitance value.