honestly, I have raise hundreds, close to a thousand chicks, and I saw this same thing. What I believe is happening is maybe over crowding? And the chicks could have piled up if there was a draft or something, and squished that chick.It's almost like it's neurologic, it doesn't have any swollen painful joints or places on its right leg or wing, it can grasp with it's foot (but not hold on) and it can pull its wing away from you when you tug it out. But ti cannot stand or balance at all, with all the weakness appearing to be on the right side.
I fine using round brooders SO much easier with less accidents.
Also there might be a coccidiosis. Look for blood in poo.