A turbine engine has inner and outer annular covers containing an annular combustion chamber and an annular nozzle. The combustion chamber is held in position inside the outer annular cover between two radial holder rings that are nested at least in part one within the other and that have their radially outer first ends secured to the outer annular cover by fasteners and their radially inner second ends in the form of combs holding in position between them a transverse rim of the annular combustion chamber so as to enable a cooling stream to flow towards the annular nozzle and so as to hold the annular combustion chamber axially while leaving it free to move at least radially.