In a known method for producing a component with a layer of transparent quartz glass, comprising: applying particles of synthetically produced quartz glass to a base body made of quartz glass and sintering the particles so as to form the quartz glass layer. Starting therefrom, in order to permit a comparatively inexpensive and reproducible production of a component with at least one layer of transparent quartz glass that is distinguished by ultrahigh purity and the absence of bubbles, it is suggested according to the invention that at least part of the SiO2 particles should be present in the form of cylindrical fragments of quartz glass fibers having a mean diameter ranging from 0.1 mm to 3 mm and a mean length ranging from 0.5 mm to 20 mm.