I cover crop my garden beds with oats, wheat, field peas, buckwheat (only if it will stay above freezing), winter vetch (for when buckwheat doesn't work), and sometimes red or white clover. Then I put hoop pens over the raised beds and run them in there. I don't worry about weeds because the chickens eat them too. 
I have 4 beds over 40' by 4'. Two were planted in fall crops, chickens not allowed because I want the lettuce and cole crops.
The other two in cover crops/green manure/chicken food. Those wiped out/pooped over beds become my spring lettuce/cole beds for spring. When the fall/winter crops are gone, they get planted in the above cover blend. Chickens wipe them out in the spring and they become my summer beds and on and on infinitum. Summer beds become spring beds, spring become fall beds. 
On top of chicken crap and whatever greenery they leave behind I add the compost made up from cleaned out bedding, feathers, heads and blood and any other greenery I can scrape together. 
The garden gets better each year.
Turnips are also a great green for chickens.