I agree, don't beat yourself up. It's always possible she would have died anyway, and you just happened to have the bad luck to be holding her when it happened. Animals are living beings, and all living beings eventually die. You can't prevent it or control it 100%. What you can do, what we all try to do, is make sure that those lives are the best they can be for as long as possible. You gave your chicken her best possible life and you were still trying to do that right up to her last moment. You can't do better than that. Give yourself credit for that. 
