Oddly enough, chairs are not listed as election materials. They are often supplied by the government or private entity from which the Polling Place is leased.
Just as anyone can walk on the carpet in the Polling Place, poll watchers can touch the chairs to move them as required.
This is not an invitation to redecorate the Polling Place. The poll watcher can move one chair in order station themself properly.
The poll watcher should keep track of that one chair and return it to it's rightful place when done, unless a substitute poll watcher will use it.
Even if something within the Polling Place is not considered election material, treat it with respect. You are a guest.