I'm working with a chick like this right now. My neighbor brought him to me at one day old; he was the sole survivor out of a bad incubator hatch. The chick's problem was an open navel and septicemia: an infection had gotten into his bloodstream before it hatched, and settled in the hock and foot of his right leg. He was in a really bad way for a while, but neither he nor I wanted to call it quits. After a month on antibiotics we finally drove the infection into hiding, but that's all it is: in hiding. At some point it's going to flare up again and it'll probably be fatal when it does. That said, the last time I had a septicemic bird (a four-month-old rooster), we got him past the primary infection and he lived for two years before dying suddenly. In the meantime, he lived fairly well, particularly considering that he should have died from his wounds. (A hawk grabbed him and really did a number on his legs and chest.)
When feeding this chick, we stumbled onto an unexpected health aid purely through dumb luck. I wanted to get some good nutrition into him (got to be a him, with that comb), so I added a little mashed-up hard-boiled egg to his chick starter. He ate it like it was going out of style, even when he was too sick to stand up. I figured that a craving like that had to be significant, and kept on supplying a little egg every day. After a few weeks, with the chick Not Dead Yet, I started to wonder. I did some research and discovered that in septicemic chicks, survival is improved on diets that are higher in protein, vitamin E, and vitamin A. Hmm. Sounds like eggs to me.
The little squirt is sitting on my lap right now, snoozing in a towel. He hatched on Thanksgiving, so he's a little over six weeks old. His feathering is free of stress marks now and the diarrhea has long since cleared up. The hock is hopelessly dislocated from all the inflammation, but no longer swollen. He hops around on his good leg with the bad one stuck wildly out to the side; it's pretty poor mobility, and we'll just have to see if his constant efforts to counterbalance damage his remaining leg or not. We've kept him indoors, and he'll never go out with the rest of the flock because they'd probably attack him. But he's imprinted as all heck, so he hardly minds that.
So there are some things that can be tried for your chick, although to be honest the best you can gain is definitely going to be a compromised bird. That said, I have built a wheelchair for a crippled rooster before, and I have to admit I'd do it again.
I'm a little nuts when it comes to chickens.