Multishell helical gold nanowires were recently imaged by electron microscopy. We show theoretically that the contact with the gold tips at either end of the wire plays a crucial role and that local minima in the string tension rather than the total wire free energy determine the nanowire stability. Density functional electronic structure calculations of the simplest and thinnest coaxial gold and silver wires of variable radius and chirality were carried out. We found a string tension minimum for a single-tube gold nanowire that is chiral and consists of seven strands, in striking agreement with observation. In contrast, no such minimum was found for silver, where the s-d competition Leading to surface reconstruction is lacking.