I am Owner of this chat room the link . The Room's title is in my native Gujarati(Indian) Language. When I created this chat room, I put public access rights on it. Now I want to change its access rights to Private, so how can I change its access rights? It is showing only one option button with text "Public" on the page.
Your rooms must be publicly readable. Private rooms are only used by moderators for specific purposes.
If you have 1000 reputation you can make your chat room publicly read-only by enabling the "gallery" setting in the access tab for that chat room.