You are unlikely to be able to create such a string/stack or whatever you wish to call it of a single atom thick string. If you could, you won't see anything. The diameter of an atom is about 1/1000th the wavelength of visible light.

There is the odd case of graphene. It is planar (two dimensional) unlike your essentially one dimensional example. Graphene is a molecule/substance that is a single atom thick consisting of carbon atoms in hexagonal sheet. You can actually see graphene, although the sheet would be much more than a single atom width...