We report that crystalline phases with ferroelectric behavior can be formed in thin films of SiO2 doped hafnium oxide. Films with a thickness of 10 nm and with less than 4 mol%. of SiO2 crystallize in a monoclinic/tetragonal phase mixture. We observed that the formation of the monoclinic phase is inhibited if crystallization occurs under mechanical encapsulation and an orthorhombic phase is obtained. This phase shows a distinct piezoelectric response, while polarization measurements exhibit a remanent polarization above 10 C/cm2 at a coercive field of 1 MV/cm, suggesting that this phase is ferroelectric. Ferroelectric hafnium oxide is ideally suited for ferroelectric field effect transistors and capacitors due to its excellent compatibility to silicon technology.