Single and two-layer InAs/GaAs(001) samples were grown in a Molecular Beam Epitaxy chamber under critical conditions, leading to the selective growth of self-assembled InAs Quantum Dot chains over mounded GaAs surfaces. Changing the thickness of the spacer layer and the InAs deposition made it possible to tune the nucleation of 2-fold or single chains in the second layer. Finite Element Method simulations evidenced the major role of the strain field in favoring the formation of single stacked chains. On the other hand, tuning properly the As-4/In flux ratio contributed to improving the QD ordering along the chains. Microphotoluminescence experiments demonstrated single photon emission properties of the observed QDs. Our growth approach did not degrade the optical quality of the InAs QDs, allowing a significant spatial correlation between the QDs aligned along the chain. (C) 2016 Elsevier B.V. All rights reserved.