If you can remove the loose piece easily then do so and clean off any old dried glue.
Glue up with woodworker's white PVA glue and apply pressure to the joint(s) by winding a double row of stout rope around the chair [put pieces of cardboard under the rope to protect the wood] and then using a short stick apply pressure to the joints by winding the rope in the manner of a tourniquet - like this...
http://img2.timeinc.net/toh/i/g/0208_tombakerskills/skill-02.jpg
Wipe off any excess glue with a damp cloth before it dries.
Joints often (mostly) work loose on chairs because people rock on the back legs - blame the rocking person.
Peccavi, January 2009
