We report results of scanning tunneling microscope measurements and ab initio calculations for Si(113). This surface is of general interest : Ge islands on Si(001) and Si(111) have (113) facets, Si(113) is thermally stable despite its high index, and it has properties of a good substrate. We bring into focus the peculiar atomic structure of Si(113) which contains a novel structural unit built around a subsurface interstitial atom. Such interstitials may be present also at other surfaces, particularly at steps, and may play an important role in atomic diffusion in the subsurface layer. The interstitials are sixfold coordinated; this unexpected result disturbs the simple picture of reconstruction driven by rebonding of dangling bonds. Our calculations indicate that the interstitials are released when the surface dangling orbitals rebond, e.g., as the result of adsorption of atomic hydrogen or during epitaxial growth.