Optical second harmonic generation (SHG), using 1064 nm excitation, has been used to probe the electronic structure of the single‐domain In‐induced 4 × 1 reconstruction of vicinal Si(111). Deposition of less than 1 monolayer of In onto a stepped Si(111) surface, held at 450 °C under ultra‐high vacuum conditions, produced a single domain 4 × 1 structure with the In chains aligned with the [‐110] step edges. On formation of the single domain Si(111)–4 × 1‐In structure, the s‐polarized SH response showed a large, anisotropic change. The nonlinear susceptibility along the chains, parallel to the step edges, increased by a factor of about 2.5 over that of Si(111)–7 × 7, while the change in the susceptibility in the surface plane perpendicular to the step edges was very small. Recent reflection anisotropy spectroscopy (RAS) studies of the same system found a dominant linear susceptibility in the surface plane perpendicular to the step edges, which was attributed to electron confinement effects. SHG and RAS are providing different, and complementary, information about this system. The SHG results are consistent with quasi‐one‐dimensional metallicity along the chains, evidence for which is seen in photoemission and inverse photoemission studies of the single domain Si(111)–4 × 1‐In structure.