Turn the chair upside down so you can access its underside. Remove any fastening hardware from the legs using a flathead or Phillips screwdriver and set them aside in a safe place. If required, use an Allen key of the appropriate size.
Inspect the top edge of each leg, where it bonds to the underside of the chair. You should see traces of old, crumbling adhesive. Using coarse-grit sandpaper, sand each top edge until you reach fresh wood.
Apply a generous layer of carpenter's glue to the freshly sanded top edge of one leg and insert it into its original place on the underside of the chair. Secure any fastening hardware. Repeat with the remaining legs.
Cut an automotive inner tube into several long 1-inch thick strips using scissors. Wrap the rubber strips tightly around each leg joint, covering the upper part of the leg and the corner of the seat. This will help clamp the leg in place while the glue sets.
Allow the glue to dry for 24 hours. Remove the the inner tube strips.