A furnace for the continuous heat treatment of glass containers, comprising a structure (12) provided with a conveyor (13) which is designed to receive containers (31, 131, 231) and which is made to advance through a hot zone (14) and a ventilated zone (15), said conveyor (13) comprising a pair of chains (17) which are located on opposite sides of the structure (12) and which are wound in an endless loop onto toothed end pulleys (18) so as to define an upper conveying section and a lower return section, links in each of the chains (17) having a plurality of brackets (21) which are arranged in a projecting manner and are directed inwards towards the opposite parallel and adjacent chain (17), said brackets having, mounted on them, cross-pieces (22) provided with a plurality of supports (28) on which at least a portion of the containers may rest.