I've started keeping my chain on the pillion seat. To stop the bag causing any damage, I've added some non slip matting.

Good idea. Looks like the tool drawer liner stuff. I'm surprised the chain will do damage though to the rear seat cover even while in another bag, but I'm sure you know what you're dealing with.

It is the very same, drawer liner.

I don't think the chain will cause any damage but the bag might. I also wanted to test out the electric stapler I was given!