You don't have to let the vet euthanize her. Please take a look at poultrypedia, and see what some of your options are. The sooner you work with her the better.
The best thing to do is to get her to a vet.
If the leg is warm it could be an infection.
Check the top of the leg for anything wrapped around it. Check carefully.
Do they have a good grippy surface to walk on? Is it possible she has splay leg?