I concur. Chestnuts are known for holding last year's leaves. That does not concern me, but the dead branches do. The fact that the rest of the tree is green and looks good is a plus. I'm not sure if it is a disease or not. I have not seen that with any of my trees. It seems the whole tree dies or it flourishes. If it were me, I would immediately prune those dead branches as soon as possible and burn them. They are not contributing to the tree, and if they do carry some disease, leaving them can't be good.
Thanks,
jack