The chick should not be eating layer feed. Layer feed has way too much calcium for chicks (about 3 times as much as they need, and that can cause problems.) Layer feed usually does not have enough protein for a growing chick, although some kinds do-- but the big issue is the calcium.
So you should get starter or grower. Either one is safe for the entire flock to eat. Just make sure they have a dish of oyster shell, so the ones that are laying can get the extra calcium to produce eggshells. Chickens are usually pretty good at eating the right amount of calcium, so don't worry if chicks or roosters sample it too: they typically won't eat enough to cause any trouble for themselves.