A gas-dispensing device (2) for dispensing a gas into breathing gas, comprising a membrane (6) through which the gas can diffuse into the breating gas, is described. The gas-dispensing device (2) is simple and reliable because it contains a self-contained chamber (4) in which the gas is held at a predefined overpressure, and the membrane (6) is arranged to form a part of the chamber's (4) wall.