Apply a wood finish stripper to the area with the dark spots using a paintbrush. Let the stripper set for the time instructed on the package.
Scrape off the stripper and melted finish with a putty knife, taking care to not put scratches in the wood. Dip a stripping pad in warm, soapy water and go over the area to remove any stripper residue. Rinse the pad in clean water, then go over the area once more to rinse.
Soak a clean cloth in household bleach and wipe down the dark spot with the bleach until the stain is gone. If the household bleach is not strong enough, apply a wood restorer to the spot according to the package directions. Wood restorers may also be labeled as deck brighteners or deck restorers.
Rinse the chair with water and towel dry. Sand the spots with a 220-grit sandpaper, following the grain of the wood, until the spot is smooth. Rub the chair with a tack cloth to remove the dust.
Apply the same finish that is on the rest of the chair to the now bare spots. Let the finish dry for 24 hours before using the chair again.