I keep forgetting that we're in the alfalfa capitol of the world, lol.The stems are not poisonous....I experienced this once with a 19 pound dog..she had eaten a stem of a non poisionous plant BUT it got lodged in her intestines and poked a hole and she went septic..Had surgery and she was good as new...
That is why I mentioned that possibility is all.........Yes alfalfa hay is YUMMIE for chickens.
Timothy hay is a bit more stemmie and less leaves...... LOL
Thats too bad you don't have access to alfalfa...