Bi nanolines self-assemble on Si (001) and are remarkable for their straightness and length—they are often more than 400 nm long, and a kink in a nanoline has never been observed. Through electronic structure calculations, we have found an energetically favorable structure for these nanolines that agrees with our scanning tunneling microscopy and photoemission experiments; the structure has an extremely unusual subsurface structure, comprising a double core of seven-membered rings of silicon. Our proposed structure explains all the observed features of the nanolines, and shows that surface stress resulting from the mismatch between the Bi and the Si substrates is responsible for their self-assembly. This has wider implications for the controlled growth of nanostructures on semiconductor surfaces.