Sometimes chicks that are hatched with genetic abnormalities manage to come out of the egg and put up an appearance of being just like the other chicks. They seem to cruise on what's left of their yolk sack, and don't begin exhibiting signs they're not normal for a week or so.
The first thing you notice is they seem to be lagging in growth. Chicks double in size every week, and these chicks become very apparent they aren't growing by the end of their first week.
Then, since they lack the ability to utilize the nutrients in the food they eat, they begin to get weak. Once that begins, they lack the energy to even eat, so they go down hill quickly from there.
This is called failure to thrive, and there really isn't much you can do. Even if you manage to get the chick to eat, they will have internal problems leading to diarrhea or constipation as their little bodies struggle to cope with digesting food. Then it becomes painful and your heart just breaks for them.
There is a small chance your chick is sick with cocci or some bacteria or virus. But the odds are more in favor of this chick of yours being a failure to thrive candidate.