In a gas turbine combustion chamber (1) cooled by means of impingement cooling, the height of the cooling duct (5) formed by the perforated plate (3) and the impingement surface (4) increases continuously in the transverse flow direction to correspond with the supply of cooling air. Tubes (7) are arranged in the cooling duct (5) on the holes (6) of the perforated plate (3) in such a way that the impingement air meets the impingement surface (4) at right angles, the height of the tubes (7) increasing in the transverse flow direction in such a way that the distance between the tubes (7) and the impingement surface (4) is constant over the complete length of the cooling duct (5). By this means, the heat transfer coefficient remains constant along the impingement cooling section and uniform removal of heat is made possible. The cooling effect can be specifically controlled by a suitable choice of the diameter of the holes (6) and the height of the tubes (7).