Question regarding vegetables and chickens

[5 Points Wingfeather]

I have a pretty specific question. I was thinking today that it would be nice if I planted some climbing vegetables outside the chicken run on the west side that could climb up the fence of the run and provide shade but that would also drop fruit for the chickens. But I don’t know which vegetables would be good for that. Cherry tomatoes? Beans? Something else? Any vegetable that I would need to avoid?

 

[nuthatched]

Chicken love them some tomaters.