Separate the broken parts of the chair leg with your fingers enough that you are able to squeeze glue between the break if the leg remains in one piece. Squeeze wood glue onto the separate broken areas of the leg if it has broken in two. Press the broken sections together.
Apply a wood clamp around the broken area of the leg so that it squeezes the break together. Wipe off any glue that oozes out with a damp cloth. Allow the glue to dry 24 hours.
Remove the clamp. Sand the repaired area of the leg lightly with a fine-grit sanding pad until the break line is no longer visible . Wipe off the sanded area with a tack cloth.
Brush a coat of touch-up wood finish over the repaired area of the leg. Allow the finish to dry at least four hours and apply a second coat. Wait 48 hours before using the chair.