A combustion chamber assembly includes a through hole on the combustion chamber wall bounded on an outer side of the wall by a hole edge and a combustion chamber shingle having a collar bounding a mixing air hole on the outer side of the wall and protruding with a first collar portion beyond the hole edge on the outer side of the wall. A cooling air opening is formed on an inner circumferential surface of a duct portion of the mixing air hole adjoining the first collar portion and extending in the direction of a combustion space, the cooling air opening leading into a cooling air duct which extends through the duct portion and via which cooling air is guided out of the mixing air hole in a direction of a hot side of the shingle facing the combustion space.