if it's an old chain check for frozen links, if it's not, check the sprocket with a poiner on the swing arm to see if it is offset or something, if it looks as though the whole sprocked is moving like it's off center, I'd tear the wheel off and check everything in the wheel.
Had one that did that, when I got the bike the sprocket was loose, no idea he rode it like that, but it wore enough that the sprocket would sit off center, when I did a quick snug up and rode it a while, I noticed it, had to get a new backer plate, sprocket was fine, but since I wanted to change ratio anyway.
ken.