Just a thought, I'm very bored at work and trying to kill time. I did try to keep the general theme of how this would work by using the same or similar in-game mechanics to how other processes work currently.
BUILDING : The coop itself is built just like a cabin, but with different materials. 50 boards, 20 blocks, 10 stone (for grit), and 20 straw.
The coop has only one level, 8x4 interior. On either side are two special, non-movable furniture items : The feeding trough, and the hatchery.
Players must catch wild chickens and release them into the coop to 'domesticate' them. Chickens within the coop will feed from the trough every 8 hours (1 in-game day). Every feeding cycle, the chicken has a 10% chance to lay an egg. The QL of the egg depends on the average QL of the water/feed eaten, and the original QL of the chicken. The eggs will disappear after one in-game day.
Eggs can be cooked by themselves (base of 1 dex FEP), hardboiled in a cauldron (base of 2 dex FEP), or cooked with any kind of cheese into an omelette (base of 10 dex FEP).
Eggs placed within a hatchery will hatch into chicks after 3 in-game days (They must be removed and dropped in the coop itself to feed), and will grow into a new chicken after an in-game week. Chicks can be butchered but only provide a single bone material. The bone material is half the QL of the full-grown chicken.
The coop's feeding trough has two fullness gauges, water and feed. It can be filled with seeds or earthworms or whatever it is that chickens eat. The more chickens in the coop, the faster the feed trough is used up. Chickens will die if unfed for 2 feeding cycles, chicks will die if they miss a single feeding cycle.
The maximum amount of chickens available in a single coop is 10. If more than 10 chickens are present, any chicks will die instantly on the next feeding cycle. If there are still more than 10 after all the chicks are dead, random chickens will die until only 10 remain. A 100% full trough will sustain 10 chickens through three feeding cycles without needing to be refilled.
All wild chickens start out at QL10, and to increase quality they must be fed with high-quality seeds/worms/whatever and allowed to lay eggs to produce higher quality chickens.
In the end, it's quite a bit of work but the rewards are higher quality feathers, more variety for dex-producing food, etc. Also a good use for all the high-quality seeds that don't get thrown out and can't be milled (Other than grass, of course). There's probably quite a few new foods that could be added with eggs, and maybe new uses for feathers (Ranger's arrows, anyone?). Anyways, please feel free to critique the shit out of this suggestion.