A linear alignment of self-assembled, cubic SiC dots grown by molecular beam epitaxy on Si substrates is demonstrated. The formation of well-ordered biatomic steps on (111) Si was used to control the nucleation sites. The resulting terraces promote an alignment along their step edges. SiC on Si represents self-organization in a system with chemical interactions. The resulting instability of the Si surface during the nucleation requires a precise control of the process conditions. By atomic force microscopy we demonstrate the achieved linear chains of SiC dots. (C) 2004 American Vacuum Society.