It is now possible to systematically engineer one-dimensional chain structures of metal atoms on silicon using self-assembly. Stepped Si(111) templates offer the opportunity to vary the chain spacing with atomic precision and to control the electron count, including fractional band filling. Two applications of chain structures are explored: 1. An atomic scale memory is constructed using self-assembled, 5-atom wide tracks that form on Si(111)5x2-Au.@footnote 1@ Extra Si atoms in lattice sites on top of the tracks are used to store data, one bit per atom with an empty buffer space of 5x4 atoms. The density is comparable to that in DNA (32 atoms/bit). This memory serves as test structure for finding the fundamental limits of data storage density and readout speed. They are given by the correlation between adjacent atoms@footnote 2@ and the shot noise in STM.@footnote 1@ 2. One-dimensional electrons in metallic chains are characterized by mapping their band structure and Fermi surface.@footnote 3@ While metallic surface electrons are completely de-coupled from the Si substrate, the metal atoms are locked into Si lattice sites which makes a Peierls transition to an insulator unfavorable. The dimensionality is varied between 1D and 2D via the chain spacing. @FootnoteText@ @footnote 1@ R. Bennewitz, et al., Atomic scale memory at a silicon surface, Nanotechnology 13, 499 (2002)@footnote 2@ A. Kirakosian, et al., Correlations in a one-dimensional lattice fluid on Si(111)5x2-Au; Phys. Rev. B, in press.@footnote 3@ R. Losio, et al., Band splitting for Si(557)-Au: Is it spin-charge separation?, Phys. Rev. Lett. 86, 4632 (2001); K. N. Altmann, et al., Electronic structure of atomic chains on vicinal Si(111)-Au, Phys. Rev. B 64, 035406 (2001); J. N. Crain, et al., Fermi Surfaces of Surface States on Si(111) + Ag, Au, Phys. Rev. B 66, 205302 (2002); J. N. Crain, et al., Fractional band filling in an atomic chain structure, Phys. Rev. Lett., in press.