A gas turbine combustion chamber, having a combustion chamber housing, a burner positioned at least partially in the combustion chamber housing and a flame tube positioned in the combustion chamber housing. An upstream end of the flame tube has a flame tube cover. In the region of the flame tube cover radially inside the flame tube cover a mixing tube of the burner extends, which defines a pre-primary combustion zone. Between the mixing tube of the burner and the flame tube cover an axial air flow passage is formed, via which air can be conducted in the axial direction outside along the mixing tube, and into the flame tube cover radial air flow passages are introduced via which the air following the axial air flow passage can be conducted in the radial direction of the flame tube cover for cooling the flame tube cover.