The early stage of adsorption of adenine on Si(111)7x7 is studied by scanning tunneling microscopy (STM). Bright protrusions are observed in both empty-state and filled-state STM images, indicative of molecular adsorption of adenine through dative bonding. The majority of these bright protrusions appear as dimer pairs formed by hydrogen bonding at the initial adsorption stage. The formation of dative bonds between the substrate and adenine and the feasibility of the H-bond mediated dimers are supported by ab initio DFT/B3LYP/6-31G++(d,p) calculations, and are in excellent accord with out recent X-ray photoemission data. Remarkably, these dimers are found to undergo self-organization into aligned superstructures, evidently with common link arrangements, including straight, offset, and zigzag chains, square quartets, double quartets, and other multiple dimer structures. As the exposure of adenine increases, the populations of dimers as well as the self-organized double dimer and other higher-order structures also increase. The end-to-end dimer links are found to be most prominent in the growth of adenine molecular chains, most notably aligned along the Si dimer-wall or [-1 1 0] direction of 7x7 unit cell. The self-aligned adenine dimer molecular chains offer a natural template for catch-and-release biosensing, lithography, and molecular electronic applications.