I have recently decided to kick it up a notch on how I store my Chanel bags. I am amazed at how they really are "investment" bags considering every bag I own is worth twice as much as I paid. So, I went to Michael's Art and Crafts and bought black felt in two sizes. I also bought velcro strips. I fashioned a felt wrap that folds into the bag and then wraps around (with notches for the chains), then it atached with velcro. I took the felt to my cleaner/tailor and they sewed the velcro on to make sure it wouldn't come off. Once the felt wrap is on I take a piece of felt and wrap the chain a few times. With my white Classic, I also put a strip of felt to keep the chain away from the white leather. I love this system, and it protect my bags from denting one another when I store them next to each other.
If possible could you post a picture ? I'm sorry I just can't picture how the felt is tucked inside.