I hope this doesn't make too much sense, but here goes:
I fold my sharp chains and wrap them individually in a shop rag like a burrito, and then they are put in the box of saw related stuff for when I go cutting.
When I swap out a chain in the field, I put the dull chain loose in the box (don't matter what happens to it since it's dull anyway) and grab a fresh sharp chain.
Plus, I now have a clean shop rag handy in case I need to wipe my hands off or clean around the bar oil cap before filling it with oil.
If there is something special about a particular chain, I write on the rag with a marker.