I also recommend grape vines. I have three vines that grow up through the center of my run and over the top. In my climate and situation the chickens would not survive without the shade the vines provide. They also provide nearly continuous forage for the chickens from spring though November. They really like the leaves. We also get well over 100 lbs of grapes every summer, which is a big bonus.
Here are some old pics of my run in spring before the vines grow out and later in early summer.


Here are some old pics of my run in spring before the vines grow out and later in early summer.

