Single-walled carbon nanotubes are hollow cylinders that can grow centimeters long via carbon incorporation at the interface with a catalyst. They display semiconducting or metallic characteristics, depending on their helicity, which is determined during their growth. To support the quest for a selective synthesis, we develop a thermodynamic model that relates the tube-catalyst interfacial energies, temperature, and the resulting tube chirality. We show that nanotubes can grow chiral because of the configurational entropy of their nanometer-sized edge, thus explaining experimentally observed temperature evolutions of chiral distributions. Taking the chemical nature of the catalyst into account through interfacial energies, we derive structural maps and phase diagrams that will guide a rational choice of a catalyst and growth parameters toward a better selectivity.