DNA nanotubes offer a high aspect ratio and rigidity, attractive attributes for the controlled assembly of hierarchically complex linear arrays. It is highly desirable to control the positioning of rungs along the backbone of the nanotubes, minimize the polydispersity in their manufacture and reduce the building costs. We report here a solid-phase synthesis methodology in which, through a cyclic scheme starting from a 'foundation rung' specifically bound to the surface, distinct rungs can be incorporated in a predetermined manner. Each rung is orthogonally addressable. Using fluorescently tagged rungs, single-molecule fluorescence studies demonstrated the robustness and structural fidelity of the constructs and confirmed the incorporation of the rungs in quantitative yield (>95%) at each step of the cycle. Prototype structures that consisted of up to 20 repeat units, about 450 nm in contour length, were constructed. Combined, the solid-phase synthesis strategy described and its visualization through single-molecule spectroscopy show good promise for the production of custom-made DNA nanotubes.