Insert wood glue into the split using a small brush or by squeezing the glue from the bottle directly into the damaged area. Be generous, as it is better to have too much glue than not enough.
Fit the split pieces together, matching up the fibers as closely as possible. Place a wood clamp over the area and adjust it to firmly hold the break together.
Wipe up any excess glue that squeezes out from the split with a clean damp cloth.
Allow the glue to dry for at least 24 hours before removing the clamp. Wait another two days before putting weight on the chair leg so that the glue has time to completely dry on the inside of the split.