We have carried out first principles total energy calculations to study the formation of InN atomic-size wires on the In/Si(111)-(4 x 1) surface. In its most favorable adsorption site, a single N atom forms InN arrangements. The deposit of 0.25 monolayers (MLs) of N atoms, result in the breaking of one of the original In chains and the formation of an InN atomic size wire. Increasing the coverage up to 0.5 ML of N atoms results in the formation of two of those wires. Calculated surface formation energies show that for N-poor conditions the most stable configuration is the original In/Si(111)-(4 x 1) surface with no N atoms. Increasing the N content, and in a reduced range of chemical potential, the formation of an InN wire is energetically favorable. Instead, from intermediate to N-rich conditions, two InN atomic wires are more stable. Projected density of states calculations have shown a trend to form covalent bonds between the In-p and N-p orbitals in these stable models. (C) 2016 Elsevier B.V. All rights reserved.