Also, cedar blocks can help repel moths, as can herbs such as lavender and rosemary. Replace blocks or sachets periodically or reactivate with drops of essential oils.
Make sure the woolens are clean before being put in the chest so no traces of food or perfume can attract moths and so you are certain there are no moths eggs on them. Also, clean the chest itself thoroughly for the same reason. Also, see if you can make the chest essentially air tight so moths can’t get in to lay eggs.
Moths like humidity so make sure the chest is not in a bathroom or other humid part of your house.
Check the contents of the chest every now and then to be sure all is still well.