We report the growth and characterization of thin (≪35 nm) germanium-carbon alloy (Ge1-xCx) layers grown directly on Si by ultrahigh-vacuum chemical vapor deposition, with capacitance-voltage and leakage characteristics of the first high-κ/metal gate metal-oxide-semiconductor (MOS) capacitors fabricated on Ge1-xCx. The Ge1-xCx layers have an average C concentration of approximately 1 at. % and were obtained using the reaction of CH3GeH3 and GeH4 at a deposition pressure of 5 mTorr and growth temperature of 450 °C. The Ge1-xCx films were characterized by secondary ion mass spectrometry, atomic force microscopy, x-ray diffraction, and cross-sectional transmission electron microscopy. A modified etch pit technique was used to calculate the threading dislocation density. The x-ray diffraction results showed that the Ge1-xCx layers were partially relaxed. The fabricated MOS capacitors exhibited well-behaved electrical characteristics, demonstrating the feasibility of Ge1-xCx layers on Si for future high-carrier-mobility MOS devices.