It is not uncommon for chicks to end up with a case of pasty butt. The buildup of poop around their vent can completely block their ability to poop, which can be fatal.
There are a number of reasons for pasty butt. The most common are stress, being too cold (mail shipping), being too hot (heat lamps), and on occasion from viral or bacterial infections.
New chicks should be inspected for signs of pasty butt and treated immediately until the condition clears up. While inspecting the chicks, be sure that you do not confuse the remains of the bellybutton with poop. Just like with new babies, chicks have a small amount of tissue that must dry up and fall off. Never attempt to pull this off, as you can disembowel them.
If you find evidence of pasty butt gently hold the chick in your hands and run luke warm water over their vent to soften the poop. Use your finger or a small piece of paper towel to gently wipe the area until all of the poop is removed. DO NOT pull the poop off. If it doesn't wipe off easily, keep using water to soften it.
It is very important to thoroughly dry the chick. You can use a blow dryer on low with warm heat. Hold it at a safe distance. You can also use a washcloth to help dry them off.
Using a Q-tip, carefully apply a small amount of Vaseline to their vent area to help prevent future poop build up. Also make sure that you are properly controlling the temperatures in their brooder box.