Using scanning tunneling microscopy, we observe an adlayer structure that is dominated by short rows of S atoms, on unreconstructed regions of a Au(111) surface. This structure forms upon adsorption of low S coverage (less than 0.1 monolayer) on a fully reconstructed clean surface at 300 K, then cooling to 5 K for observation. The rows adopt one of three orientations that are rotated by 30◦ from the close-packed directions of the Au(111) substrate, and adjacent S atoms in the rows are separated by √ 3 times the surface lattice constant, a. Monte Carlo simulations are performed on lattice-gas models, derived using a limited cluster expansion based on density functional theory energetics. Models which include long-range pairwise interactions (extending to 5a), plus selected trio interactions, successfully reproduce the linear rows of S atoms at reasonable temperatures.