Some of my rabbits will eat it but others won't. I read that it should be cut across the stalk into small pieces to prevent a rabbit from accidently getting the strings tangled in their back teeth.
Mine all LOVE the leaves - I make sure there is no brown on them tho.
They also like the tiny little stalks at that top or in the parts where leaves grow. I don't give the larger pieces to them cause the strings are too thick.