We investigate the self-formation of Si atomic lines and dimer vacancy chains on the beta-SiC(100) surface by atom resolved scanning tunneling microscopy (STM). We show that, using a rigorous protocol in surface preparation, it is possible to build very long, very straight and defect-free Si atomic lines. These lines are derived from the dimer rows of the beta-SiC(100) 3x2 surface reconstruction by selective Si removal resulting, at the initial step, in very long dimer line vacancies. Using the capability of the scanning tunneling microscope to probe simultaneously both filled and empty electronic states, we confirm that these atomic lines are composed of Si-Si dimers perpendicular to the line direction. These Si atomic lines are derived from the beta-SiC(100) 3 x 2 surface dimer rows by surface thermal dismantling including, at the initial step, Si removal "dimer row by dimer row" leaving very long dimer line vacancies. On the 3 x 2 surface, the Si-Si dimers are asymmetric in marked contrast with the dimers forming the Si atomic lines that are symmetric. Such a behavior is understood in terms of decreased lateral interaction between atomic lines when the spacing between them is increased. These highly stable atomic Lines reveal a novel aspect of SiC in its ability to also be a very suitable material in nanotechnologies and micro/nano-electronics of the future.