Hen has no balance to stand or walk but seems bright and alert
She may have laid a lash egg. There are many threads about lash eggs with pictures if you do a search at the top of the page. Have you added any new birds to your flock recently? Was she vaccinated for Mareks disease? Sometimes there can be a temporary paralysis from laying an egg. Has she been laying recently? She may be an internal layer, especially if that was a lash egg, and that can lead to egg yolk peritonitis. I would make sure that she is eating and drinking, maybe add some vitamins to her water, and give her a little bit of chopped egg to eat.
Most vets don't treat chickens unless they have a special interest in them. Here are a few articles to read about egg yolk peritonitis and internal laying:
The following are from the Merck Manual about various illnesses of the reproductive tract:
Edited by Eggcessive - 3/16/16 at 6:53am
You're welcome. I'm all for vet help if you can do that. Baytril or enrofloxacin are best for EYP, but they are against FDA regs for chickens, although your vet may have a good option. Some vets will quietly prescribe if the chicken won't be used for food, and you can order it online here: http://www.backyardchickens.com/t/959119/baytril-enrofloxacin-sources