Is there any way you could see a vet tomorrow for an xray to rule out a fracture? How old is she? Was she vaccinated for Mareks? Did you witness her injury, and lastly do you have a rooster? This is a pretty serious injury, but there could be some nerve damage, and I worry a little about Mareks diseases or curled toe paralysis. If it is an upper leg injury, those apparently are hard to splint, since splinting should be done both above and below the injury.
I would say if you used a sling, she should be suspended off the floor with neither leg touching the floor. Slings are usually meant for periods throughout the day, then letting them sleep at night lying down, but I really am not sure if that would be best for your chicken. Here is a video of a type of sling: