Chickens cost 1500G and are fed Chicken Feed (10G per bag, purchased at the Green Ranch). Alternatively, they can be left outside and will feed themselves. However, they will get sick if they are left outside during the Winter or on a rainy day, if they are beaten, or if they are not fed when indoors. Chickens take 1-2 days to recover from being sick.
Each chicken produces one egg a day, assuming that they are not-sick. Each egg is worth 50G; alternatives to selling the egg include: feeding it to your dog, giving it as a gift (Elli and Cliff, in particular, will enjoy these), offering it to the Harvest Goddess, or incubating it for another chicken.
Eggs take three nights to hatch into chicks. Chicks take 7 days to grow into a chicken. During this time, they do not need to be fed and can die if they are left outside in a typhoon.
StrategiesIt is a common strategy to save up your money (don't buy any crops) for the first week in the game in order to purchase a chicken right away. Assuming you buy a chicken by the Spring-7, you can have all six chickens by Summer-25. Some people like to keep their chickens outside in order to save money on feed (a common favorite place it keeping them on your roof, after purchasing the stairway), but most will generally pay for food, in order to take care of the chickens inside (where time does not pass).