The synthesis of fully epitaxial ferroelectric Hf0.5 Zr0.5 O2 (HZO) thin films through the use of a conducting pyrochlore oxide electrode that acts as a structural and chemical template is reported. Such pyrochlores, exemplified by Pb2 Ir2 O7 (PIO) and Bi2 Ru2 O7 (BRO), exhibit metallic conductivity with room-temperature resistivity of <1 mΩ cm and are closely lattice matched to yttria-stabilized zirconia substrates as well as the HZO layers grown on top of them. Evidence for epitaxy and domain formation is established with X-ray diffraction and scanning transmission electron microscopy, which show that the c-axis of the HZO film is normal to the substrate surface. The emergence of the non-polar-monoclinic phase from the polar-orthorhombic phase is observed when the HZO film thickness is ≥≈30 nm. Thermodynamic analyses reveal the role of epitaxial strain and surface energy in stabilizing the polar phase as well as its coexistence with the non-polar-monoclinic phase as a function of film thickness