Hafnia-based thin films are a favoured candidate for the integration of robust ferroelectricity at the nanoscale into next-generation memory and logic devices. This is because their ferroelectric polarization becomes more robust as the size is reduced, exposing a type of ferroelectricity whose mechanism still remains to be understood. Thin films with increased crystal quality are therefore needed. We report the epitaxial growth of Hf0.5Zr0.5O2 thin films on (001)-oriented La0.7Sr0.3MnO3/SrTiO3 substrates. The films, which are under epitaxial compressive strain and predominantly (111)-oriented, display large ferroelectric polarization values up to 34 mu C cm(-2) and do not need wake-up cycling. Structural characterization reveals a rhombohedral phase, different from the commonly reported polar orthorhombic phase. This finding, in conjunction with density functional theory calculations, allows us to propose a compelling model for the formation of the ferroelectric phase. In addition, these results point towards thin films of simple oxides as a vastly unexplored class of nanoscale ferroelectrics.