We present a tight-binding molecular-dynamics investigation of the geometrical and the electronic structure of suspended monatomic noble-metal chains. We show that linear monatomic chains are formed at temperatures equal to or smaller than 500 K for Au, 200 K for Ag, and 4 K for Cu and that they are stable for at least 10 ns. We also evidence that such stability is associated with the persisting $sd$ orbital hybridization along the chains. The study highlights fundamental limitations of conductance measurement experiments to detect these chains in the breaking process of nanowires.