Lee Schierer McKean, PA
Forget the wood swelling liquid, metal grippers and gorilla glue. Here's what I did after seeing all of those methods fail.

I carefully remove the tenon and clean off any old glue. Then I clean out the socket, even drilling the hole slightly larger. I take a piece of clear soft maple and my sharp bench plane. I shave off some long fairly thick shavings. Then I coat the tenon with glue and wrap the shaving around the tenon, applying glue as I wrap it until it is slightly larger than the socket hole. I tightly wrap the wrapped shaving with as many rubber bands as I can get on it to "clamp" the shaving in place. Once the glue sets up I remove the rubber bands and carefully file down the tenon for a very snug fit. Then I apply glue to both surfaces (tenon and socket) and assemble the chair insuring that I place it on a level floor so that all legs touch while the strap clamp does its work.

I've had chairs repaired with this method last for years before needing additional repairs.

Lee