The japanese honeysuckle sounded like a great idea... however after googling it it seems as if its a super invasive alien plant and can choke out other vegitation. The site i looked at recomended trumpet honeysuckle as an alternative. I like the idea of something mice and smelly. :)
If you were thinking of bamboo.... there are two dif ways bamboo propigates sme by runners ( which will take over everything) and some grows in clumps which may work for your scenerio as it grows fast and thick... but there are very interesting varieties of both.
Since my simple chicken run project has since turned into the chicken version of fort knox I may use a mix of the suggested vines and perhaps one grape vine, i just think it would be fun to watch chickens try to fly up to eat grapes. lol