The chickens love my compost pile, but, i can't help you. I do not know anything about enclosed chicken runs and composting beside it in a bin. If you have information about that I would like to read it for my own education.
Actually the way I intend to set it up is to have the compost dumped on a corner of the outside run. Might be boxed in a bit. Not sure yet. There are threads on this site that go into details about it. One of them was highlighted on the home page.