A "bug doctor" might be helpful.

Unless the chest has some special antique value, chuck it.

Totally agree.

In England we used to refer to this problem as wood worm, although it`s not really a worm but a sort of beetle.

If you are not careful, the wood worm will soon affect everything else made of wood, including doors, tables, chairs and wooden staircases in your home and once it begins to spread it starts to eat and powder the wood from the inside out and almost impossible to cure.

My advice is to burn the chest and then check that it has not spread elsewhere within your home.