How short do you want to go? I would just go to the local hardware store and buy two small rings that you can then run through the two pieces of chain on either side. Just make sure the ring is big enough to catch on the holes exiting the top of the bag so it acts as a stopper.
And be mindful that this approach might scratch the chain unless you can use plastic zip ties or something non- metal. Actually plastic zip ties aren’t a terrible idea (although not the greatest look when open)