The success of silicon as a dominant semiconductor technology has been enabled by its moderate band gap (1.1 eV), permitting low-voltage operation at reduced leakage current, and the existence of SiO2 as a high-quality "native" insulator. In contrast, other mainstream semiconductors lack stable oxides and must rely on deposited insulators, presenting numerous compatibility challenges. We demonstrate that layered two-dimensional (2D) semiconductors HfSe2 and ZrSe2 have band gaps of 0.9 to 1.2 eV (bulk to monolayer) and technologically desirable "high-κ" native dielectrics HfO2 and ZrO2, respectively. We use spectroscopic and computational studies to elucidate their electronic band structure and then fabricate air-stable transistors down to three-layer thickness with careful processing and dielectric encapsulation. Electronic measurements reveal promising performance (on/off ratio > 106; on current, ~30 μA/μm), with native oxides reducing the effects of interfacial traps. These are the first 2D materials to demonstrate technologically relevant properties of silicon, in addition to unique compatibility with high-κ dielectrics, and scaling benefits from their atomically thin nature.