Hard to combat the chickens!
I say let the weeds grow! Many of them are healthy for the chickens, for people, and good to encourage the bees. Plus, when you get hit with a drought, the weeds tend to stay green long after those perfectly manicured lawns turn brown.
Now, I don't know what you could plant that would be able to establish itself before the chickens make short work of it, but some healthy choices of 'weeds' could be:
Dandelions - the greens are full of vitamin A and C. A cup of steeped dandelion greens gives you the same C as a half a cup of orange juice. They are a bitter green, but go nice In a summer salad or lightly stir fried like you would broccoli raub.
Plantain (the leafy green, not the tiny banana) - also a healthy dark green, but if you crush the raw leaves up in your hand, the juice is a mild astringent that helps sooth bug bites.
Clover - excellent for bees
Sorrell - a partial food source, but the little yellow flowers are charming.
Purslane - fleshy green that is great in a Greek salad and grows like a weed! Great to plant with other things because it draws up nutrients from the soil that helps the other plants nearby.
Lady's Thumb, grape hyacinth, many other types of weeds that ... if we can figure out how to get the chickens to give the lawn a break, can grow wild and well in even poor soil.
On the edges of the property (if it is not too overly suburban) encourage the taller wild plants like goldenrod, queen Ann's lace (wild carrot), onion grasses, wild garlic, thistle and the like ...
No pesticides? No fertilizer? No problem for a whole lot of these plants that most folks (for some reason) actively try to REMOVE from their environments!
If you can get a Few of these established in your bare spots, they will pave the way for other plants to return ... hopefully resulting in more forage than your chickens can manage!
