Two-dimensional semiconductors could be used to fabricate ultimately scaled field-effect transistors and more-than-Moore nanoelectronic devices. However, these targets cannot be reached without appropriate gate insulators that are scalable to the nanometre range. Typically used oxides such as SiO2, Al2O3 and HfO2 are, however, amorphous when scaled, and 2D hexagonal boron nitride exhibits excessive gate leakage currents. Here, we show that epitaxial calcium fluoride (CaF2), which can form a quasi van der Waals interface with 2D semiconductors, can serve as an ultrathin gate insulator for 2D devices. We fabricate scalable bilayer MoS2 field-effect transistors with a crystalline CaF2 insulator of ~2 nm thickness, which corresponds to an equivalent oxide thickness of less than 1 nm. Our devices exhibit low leakage currents and competitive device performance characteristics, including subthreshold swings down to 90 mV dec−1, on/off current ratios up to 107 and a small hysteresis. High-performance MoS2 transistors can be created using 2-nm-thick CaF2 as a gate insulator, which forms a quasi van der Waals interface with the 2D semiconductor.