The epitaxial growth of multifunctional oxides on semiconductors has opened a pathway to introduce new functionalities to semiconductor device technologies. In particular, ferroelectric materials integrated on semiconductors could lead to low-power field-effect devices that can be used for logic and memory. Essential to realizing such field-effect devices is the development of ferroelectric metal-oxide-semiconductor (MOS) capacitors, in which the polarization of a ferroelectric gate is coupled to the surface potential of a semiconducting channel. Here we demonstrate that ferroelectric MOS capacitors can be realized using single crystalline SrZrxTi1-xO3 (x = 0.7) that has been epitaxially grown on Ge. We find that the ferroelectric properties of SrZrxTi1-xO3 are exceptionally robust, as gate layers as thin as 5 nm corresponding to an equivalent-oxide-thickness of just 1.0 nm exhibit a ~ 2 V hysteretic window in the capacitance-voltage characteristics. The development of ferroelectric MOS capacitors with nanoscale gate thicknesses opens new vistas for nanoelectronic devices.