We have fabricated hysteretic YBa2Cu3O7 step-edge junctions on LaAlO3 substrates by shunting our intrinsically over-damped junctions with a monolithic capacitor. By comparing the I-V curves of junctions fabricated on the same substrate with and without capacitor counter-electrodes, we are confident that the observed hysteresis is due to the shunting capacitor. The capacitor consists of a dielectric layer (SrTiO3 or LaAlO3), deposited on the YBa2Cu3O7 directly over the step-edge junction and a Ag counter-electrode. Capacitor counter-electrodes ranging in area from 10 mu m x 30 mu m to 200 mu m x 220 mu m have been investigated. We have used dielectric layers several tens of nm's thick. The resulting I-V curve is roughly that expected from the Stewart-McCumber analysis for the case of a voltage-independent shunting resistance. The inferred beta(c) values are as large as 10 at 4 K and decrease with increasing temperature. At 65 K, beta(c) of 1.3 was observed. The inferred beta(c) is smaller than one naively calculates from the measured junction resistance and expected shunt capacitance. We discuss likely reasons for this disagreement.