A process and a device for coating the inner surface of a greatly arched, essentially dome-shaped substrate by CVD are described. In the process, the reaction gases, which contain the layer-former molecules, are conveyed into the reaction chamber containing the substrate(s) to be coated, through at least one gas inlet, placed facing the vertex of the dome at a distance from the surface to be coated. Deposition of the layer material on the substrate is brought about in a way known in the art by producing a reaction zone on the inner surface of the substrate to be coated. According to the invention, the reaction gases do not, as is usual for known processes, flow slowly into the reaction chamber. Instead, for production of a uniform coating, the reaction gases are introduced into the reaction chamber at a high speed such that the product of Reynolds number, R, of the gas jet in or in the immediate vicinity of the gas inlet and the distance, h, between the gas inlet and the dome vertex is:400