Good question! Typically, you don't want your chicks to eat layer feed since it has too much calcium for them, and you don't want your laying hens to eat too much chick starter because it lacks the calcium they need to produce strong egg shells. However, if your birds are kept in the same area, it's virtually impossible to guarantee your birds will eat the right feed (and with typical perversity, they are usually drawn to the feed you don't want them to eat!)
If you have birds of different ages that may have different dietary needs, there is a way to manage, however. You may want to switch your whole flock to a grower/developer feed temporarily. Grower/developer doesn't have all the calcium that is found in layer feed, so it will not cause problems with too much calcium being consumed by growing birds who are not using it to produce egg shells. For your layers, though, you will want to make sure you are also offering oyster shell free choice (separate from your feed) in case they need the supplementation for producing good, hard egg shells. Using grower/developer and offering free choice oyster shell is a good compromise that will meet the needs of chickens who are at different levels of maturity and with different nutritional needs.
A note on medicated feed: Some may have heard that the eggs of laying hens that have consumed medicated chick feed are unsafe to eat. Most medicated feeds contain amprolium, a medication which inhibits the absorption of thiamine in the protozoa that causes what is known as coccidiosis. The FDA does not recommend a withdrawal period for amprolium, meaning eggs can immediately be consumed from hens that have eaten feed medicated with amprolium. However, amprolium can be found in egg whites and yolks up to 10 days after the medication is removed, but the level does not exceed the U.S. tolerance level of 8 mg/kg. We advise individual discernment as to whether or not to eat the eggs of layers eating medicated feed since amprolium blocks thiamine absorption.