It depends somewhat what your soil and sun and so forth are like.
But, for an average-good mostly-sunny site that is not on serious clay, some reasonable options would include (in no particular order)
ninebark (the species, not fancy-leaved cultivars; it will grow too big for a small run but for an ample full-height run will be ok and you can always just let it grow out thru the run fence mesh)
forsythia (ditto on size), unless you are in a cold enough zone that forsythia does not do well there
bush-type willows (ditto on size, for some of them; prefer damper rather than drier site)
lilac (ditto on size but can control easily with pruning if desired)
red osier dogwood (ditto on size but can easily control with pruning if desired)
No guarantees on any of these but they include most of your 'usual suspects' that MIGHT work for you. (there are others that might work too, I've just listed what I'd consider the best bets, that I can think of offhand anyhow). For any of these, you would be best off protecting the area around their roots (to a signfiicant distance!) with some large pavers or big stones or something like that, so the chickens cannot scratch up the newly planted rootball and can't do too much damage to the roots on an ongoing basis.
Good luck, have fun,
Pat