Chickens cost 1,500G and are fed with Chicken Feed (at 10G each), you can buy both of these from the Poultry Farm.
Chickens need to be fed every day to not get sick (While in Chick stage, they do not need to be feed). It will take 2 days for a Chiken to recover of its sickness. Chickens will not produce eggs while sick even if fed. You can put the chicken feed in any order in the bins.
Eggs are worth 50 G each and can be sold or used to hatch more chickens. You can breed more chickens by putting an egg in the incubator located in the chicken coop. It takes a 3 days for an egg to hatch and 9 days for it to grow up and start producing more eggs.
Chickens start producing Small Eggs then Medium Eggs and, with max affection, Large Eggs. To get Gold Egg laying Hen, your Chicken must win the Chicken Sumo Contest. These do not affect the cost of the eggs but the result on the maker.
If Chickens are left outside, they do not need to be fed, there is a risk to be attacked by a stray dog so you should leave your dog oustide, too.
Every day you should hold your Chicken once (any aditional won't have any effect) to raise its affection. Not feeding your Chicken, leaving outside on rainy or snowy days, attacking it with your tools and being scared by the stray dog will reduce its affection.