High-performance logic based on carbon nanotubes (CNTs) requires high-density arrays of selectively placed semiconducting CNTs. Although polymer-wrapping methods can allow CNTs to be sorted to a >99.9% semiconducting purity, patterning these polymer-wrapped CNTs is an outstanding problem. We report the directed self-assembly of polymer-coated semiconducting CNTs using self-assembled monolayers that bind CNTs into arrays of patterned trenches. We demonstrate that CNTs can be placed into 100 nm wide HfO2 trenches with an electrical connection yield as high as 90% and into 50 nm wide trenches with a yield as high as 70%. Our directed self-assembly method is an important step forward in pitch scaling.