We were able to significantly improve the quality of the heteroepitaxial films of the cubic modification of silicon carbide, 3C-SiC, by the use of organosilicon precursors and a careful control of the initial stage of the growth. The films were prepared by chemical vapor deposition from an organometallic precursor, methyltrichlorosilane. It is shown that the interfacial stress, which originates from the large lattice mismatch between the silicon substrate and the SiC film, efficiently relaxes with increasing distance between the interface yielding thick films of high quality for a thickness of greater than or equal to 20 mu m.