Hoppes #9 is an ammonia based solvent, which does a good job attacking copper.  Many times in plating, they use a thin coat of copper so that the chrome adheres better.  The worry is that the solvent will eventually lift off the chrome.

I have never seen Hoppes #9 destroy a chrome lined barrel because the solvent is cleaned out rather quickly.  I did read about a nickel plated revolver that was left to soak in a jar of Hoppes and the nickel plating all flaked off.

I would have no problem using Hoppes in a chrome lined barrel.  I just wouldn't let it sit and soak in it.