If you already have the run and it is one piece- which is how mine are- can you put the coop inside up on blocks? You might have to pick up the kennel and put it over the house, since Im sure it wont fit through the door. This will keep you from having to cut a hole in the chain link. Otherwise, if you find yourswlf with no other choice, you use bolt cutters and cut a hole just big enough to fit around the door. This will allow the chianlink to keep its shape. Then secure every link to the house.
here is a pic of mine...
here is a pic of mine...

