3 day old chick limping and keeping leg extended
IIRC, this can be a nutritional deficiency. Try giving a poultry specific vitamin supplement in their water, such as Sav-a-Chik or Liquid Poultry Nutri-drench. Probiotics are not a bad idea either.
I assume they were shipped? Shipping is extremely stressful on them, I'll never do it again as we lost over half of them because we didn't know to give them the vitamins and probiotics right away. As soon as we gave them that (after two days of them dropping like flies), they starting bouncing back.
The link below mentions vitamin B's being specifically important for leg problems. Vitamin B also gets used up a lot during stress.