How can you get the smell of mothballs out of a chest of drawers?

Wipe the inside of the drawers with vinegar. Lay some charcoal in each drawer for a few days. Baking soda and coffee grounds will work too.

wash it down with white vinegar, place open boxes of baking soda, coffee grounds, deactivated charchol,or cedar chips inside

Try using newspaper crumpled into balls. Put activated charcoal that you would use in a fish tank in with the newspaper. Shut the lid and leave for a week. You may need to do this a few times.

After scrubbing them well, I would dry the drawers in the sun.

Putting the drawers out in the fresh air and sunshine would help some too.

Try Febreeze.........