Ferroelectric PbZr0.2Ti0.8O3/YBa2Cu3O7 heterostructures have been grown on single crystal LaAIO3 and on buffered  Si. The cuprate superconductors are used as metal-like bottom electrodes for the subsequent growth of the ferroelectric PZT thin film. Structural studies using x-ray diffraction, and transmission electron microscopy show that the PZT layer is free of large angle grain boundaries (i.e., single crystal-like). Rutherford backscattering studies reveal the composition of the PZT layer to be close to that of the target. Ferroelectric hysteresis measurements using both pulsed measurements and a variable frequency Sawyer-Tower circuit yield remnant polarization values (at 5V) in the range of 15-45μC/cm2 (depending on deposition conditions) with a coercive field in the range of 80-120kV/cm. At a cycling voltage of 5V, these heterostructures exhibit a fatigue lifetime of better than 2x1010 at 40kHz (the polarization decays by only 20% of the initial value). Pulsed poling experiments before and after show that the loss of polarization is reversible. These heterostructures also show excellent aging and logic state retention characteristics.