Thin films of CuxS are grown by chemical vapor deposition using Cu(thd)2 (thd = tetramethylheptanedionate), H2S, and H2 as the precursors. A deposition profile, not caused by depletion of the precursors, is present in all films. Hydrogen is needed for growth to occur; in atomic layer deposition of CuxS the reaction between Cu(thd)2 and H2S does not require H2. To explain these observations, a model is derived on the basis of competitive adsorption of Cu(thd)2 and the reaction product Hthd at the surface. With numerical calculations, the growth rate, the Cu(thd)2 concentration, and the Hthd concentration as a function of the flow axis can be simulated. A deposition profile due to competitive adsorption of Cu(thd)2 and Hthd is found.