Epitaxial ferroelectric HfZrO films have been successfully integrated in a capacitor heterostructure on Si(001). The orthorhombic HfZrO phase, [111] out-of-plane oriented, is stabilized in the films. The films present high remnant polarization P close to 20 μC/cm, rivaling with equivalent epitaxial films on single crystalline oxide substrates. Retention time is longer than 10 years for a writing field of around 5 MV/cm, and the capacitors show endurance up to 10 cycles for a writing voltage of around 4 MV/cm. It is found that the formation of the orthorhombic ferroelectric phase depends critically on the bottom electrode, being achieved on LaSrMnO but not on LaNiO. The demonstration of excellent ferroelectric properties in epitaxial films of HfZrO on Si(001) is relevant toward fabrication of devices that require homogeneity in the nanometer scale, as well as for better understanding of the intrinsic properties of this promising ferroelectric oxide.