Using density-functional theory within the generalized gradient approximation the interaction between atomic Si and the Cu(1 1 0) surface is investigated. Various structures of on-surface adsorption as well as surface-substitutional adsorption for a wide range of Si coverage are considered. Our results shows that the Cu(1 1 0) surface is active towards adsorption of Si. The energetically most preferred structure is the c(2 × 2)-Si/Cu(1 1 0) surface alloy. The reason that (2 × 2) Si chain can form on c(2 × 2)-Si/Cu(1 1 0) surface is due to the particular stability of c(2 × 2)-Si/Cu(1 1 0) surface.