A new, simple method is described resulting in the growth of cubic SiC on Si. Thermally oxidized Si(100) wafers annealed in a CO-containing atmosphere at 1190degrees C for several hours show epitaxial 3C-SiC grains, formed at the SiO2/Si interface, growing into the silicon crystal. After 3 h the SiC grains have a diameter of 25-50 nm and a width of similar to20 nm. They contain very few visible defects, and no void between the grain and the Si matrix can be observed. After 20 h, the size of the epitaxial SiC grains doubles, but the density of grains remains about the same. At 900degrees C no SiC grain formation is observed.