The constant level filler spout comprises a spout body comprising: an annular connection portion configured to press in leaktight manner against the neck of a container, co-operating therewith to define a delivery zone; a delivery duct connected to a liquid feed source via a delivery valve and opening out into the center of the delivery zone; and an exhaust vent connected to an exhaust orifice via an exhaust valve and opening out into the periphery of the delivery zone.