If you are doing it for the health, I'm not sure which part of the animal you are referring to, lol, but chicken broth is just boiled chickens. So it's essentially a chicken. So I don't really understand your question.
If you are asking if it is ok for a vegetarian to have chicken broth, then yeah, but you won't be a vegetarian because it is boiled flesh. But if you are asking if it risks things like salmonella and food poisoning like from poorly handled meat, you probably don't have nearly as much risk involved as you would actual meat.
Is that what you are looking for?