I have a similar situation with one of my young RIR girls. She mysteriously started limping last month, at about 4 months old, and I have not been able to figure out what's wrong with her. She's eating and drinking normally, and seems pretty lively, despite her condition.
The one other thing I noticed with mine was that she not maturing like her sister of the same age and breed.
Some things I tried (sadly without success):
1) extra vitamins (first liquid children's multi-vitamins and then poultry nutri-drench) administered by dropper directly in the beak
2) extra food: mix of cooked oatmeal, plain yogurt and fruit
3) de-worming
None of these things have allowed my chicken to heal or to grow any bigger. But, they came through a lot of Internet searching and research, so it's possible they might help you. The first two treatments were in case my chicken had Rickets, and the second was because she was not growing or gaining weight, so I thought she might have a parasite.
Have you looked at your chicken's poop? Apparently, worms or cocci have been known to weaken a chicken's legs.
There are also some good posts about splinting a chicken's leg with popsicle sticks, if you think that would help.
Honestly, I have kind of given up on curing my girl. She seems decently happy and can get around by flapping her wings, balancing against things and hopping. The main issue, beyond mobility, is that her butt gets really poopy. We have to wash her off with the hose occasionally.