I think the best way is to use a jewelry padding. The padding has 2 cuts at the top where you can secure the chain without having to use any tape.
If you want to do it yourself you may try with foam, which is thick and firm, allowing you to cut the spaces for the chain.
I found this site where they sell it, it's in the UK, although you might find it in any diy store near you:
http://www.twfoam.co.uk/I'm using some boxes that I bought some time ago, and they came with the padding, but I'm planning on doing them myself, so I'll definately want to try the foam.
I've also found this type of foam on Etsy, which I think it's perfect!
http://www.etsy.com/listing/92399150/the-best-needle-felting-foam?ref=sr_gallery_18&ga_search_query=...Happy packaging!