By using reflection high-energy positron diffraction (RHEPD) and first-principles calculations, we investigated an In/Si(111) surface on which the quasi-one-dimensional In atomic chains that exhibit the metal–insulator transition were formed. From the analyses of rocking curves, we found the transformation of the zigzag chain structure of In atomic chains to hexagon structures below 130K along with the phase transition from the 4×1 to the 8×2 periodicities. The band structure calculated with the optimum hexagon structure displays the gap opening of 60meV, which indicates the semiconducting character. This confirms the recent theoretical prediction that the hexagon structure is energetically favored at low temperatures [C. González, F. Flores, J. Ortega, Phys. Rev. Lett. 96 (2006) 136101].