Turn the chair upside down. Rub off any old glue that remains on the end of the chair leg with a piece of sandpaper. If you can reach into the hole the leg was set inon the bottom of the seat, rub off any old glue in the hole.
Wipe the end of the chair leg with a damp cloth until the wood changes color. Wipe the inside of the hole on the bottom of the seat until it changes color. This wets the wood so it swells.
Apply a bead of polyurethane glue around the end of the chair leg. Push the chair leg into the hole in the bottom of the furniture. Hold the leg in place and turn the chair over.
Sit the chair on a level surface. Make sure the legs are even. Put a stack of heavy books in the seat of the chair to put pressure on the leg. Leave the chair in place for at least five hours so the glue can cure.