From the cloaca.
The Chicken.
The egg in a female frog is passed through the oviduct. After that, it passes into the uteri, and finally, into the cloaca.
Egg-laying mammals, known as monotremes, have a cloaca.
Cloaca
It is where the eggs come out.
Chicken defecate (poo) from their Vent. The vent is also known as the cloaca. The cloaca is a dual purpose organ located under the tail of the chicken. Eggs come from the same opening in their body but the waste opening is closed off when the chicken lays an egg.
the term egg bound refers to a condition in laying hens where a hen is unable to pass an egg that has formed. The egg may be stuck near the cloaca, or further inside
Egg bound hens need a quiet,warm safe area to nest. Separate the bird from the rest of the flock, allow plenty of water ( with a soluble tonic) and undisturbed rest. If you can feel an egg in the cloaca and the above method does not work within 24 hours, you can lubricate the cloaca with petroleum jelly to aid in release of the bound egg. Be very careful not to break the egg.
If you mean the vent or the chickens cloaca where the egg comes out then you do not want to cure this. Moist cloaca is a sign of a healthy hen and it should always be "wet". A dry cloaca is a sure sign of either an old hen or a hen that is going to have problems laying eggs.
The cloaca is the chicken's equivalent of a rectum and genitals. The anus of a hen is at one end of the cloaca, at the posterior end of the animal. It functions in reproduction, as the site of mating and egg-laying. It also has an intestinal function and is part of the urinary tract, as both urine and faeces are excreted through it.
The vent is also called the cloaca. The cloaca is the common multi purpose organ for mating, egg laying (hens only) and fecal matter. The vent is located just under the chickens tail feathers. For roosters the cloaca is the site of the internal sexual organ.