Looking for tips on felting a storage box

I have an old chess storage box that I'd like to add felt to for better protection of the pieces.  It's not too big: about 5" X 3-1/2" X 9", and has a removable divider.  I would appreciate any links to good sources of adhesive-backed felt, and also advice on how to do this.  I'm fairly handy, but can foresee getting frustrated with trying to perfectly place pieces of adhesive-backed material inside a small box. If anyone has done this and has tips, that would be great.  Here is the box I want to line:

Just go to a Lowes or Home Depot and get some soft shelf liner.Those places should have what you need.

Good luck

I'm in the UK and used Amazon. You might find something on there. The stuff I used was more of a velvety feel than felt though but just wanted it for an old draughts set I didnt want to scratch my wooden board.

The box is pine with a divider made from balsa(?). They are both pretty soft woods. Much softer than the hard boxwood pieces inside. There is more chance of damage from the individual boxwood pieces rattling against each other than the pine box. 

I recommend super sharp scissors or an exacto blade with metal ruler/straight edge.

https://www.amazon.com/self-adhesive-felt/s?k=self+adhesive+felt

https://www.rockler.com/pressure-sensitive-felt-sheets

https://www.michaels.com/creatology-peel-and-stick-felt/M10572180.html

Since the divider is removeable you can take that out and apply the felt and trim with an exacto knife.

Cut the bottom piece and put that down. Do the same for the top.

Then do the inside front and back, then do the sides. 

Measure twice, cut once. 

As @Panwerai states, an exacto knife and a metal ruler straight edge will be your friend. 

I understand what you are trying to do and couldn't disagree with you. I for one hate it when the pieces are piled up together. I just can't allow my reproductions to be stored this way. However, I want to offer a different perspective for you to consider.

Recently, I have been into vintage Lardy and Chavet sets. I have purchased 5 sets as of today. These sets all came with small unfelted boxes where the pieces needed to be piled up together to fit in the box. Even with my OCD kicking in over-drive, I managed to allow myself to store these old sets piled up in the original box. What helped me was the realization that my 3.75" Lardy set from the 70s was stored piled up in a box for 50 years. Despite the pieces banging against each other during that time, the set remained in excellent condition. I concluded it will probably be ok if I continue to store it that way. Regardless, I still can't do it with my reproductions though. It is just a thought to consider.

Thanks, everyone, for all the useful tips and observations.

I also have a 50 year old Lardy,stored in the original unfelted box.Not a mark on any piece.

Mine is even a bit older...but it's a set I'm giving to a grandson and I'm thinking a little extra protection inside the box won't hurt.  

If he's anything like my 9 year old grandson,you'll need it.😉