Green Chicken Coop Design.
Side view, front view, and overhead view. Not exact in size or angles, but an idea of what one could do.



Although I'm not -quite- sure how I'd keep the earth on the roof and sides of the structure, I think this would be an excellent idea.
The gray color is concrete (keeping the coop stable and the chickens safe from burrowing creatures and those that might attempt to dig). Of course, as you can see, the criss-cross pattern is wire and/or hardware cloth. Inside are nest boxes and roosts.
A slight difference, I believe, from most coops is that the "pop door" is set -in- the human door. I think this gives more room inside for positioning waterer(s) and so forth because whenever a door is built, you have to allow a certain amount of space around that door for the invisible hallway it creates. A bit too interior design-ish perhaps, haha. Anyway, this could also make the coop safer from predators that might attempt to get inside (after possibly crossing the fortified fence of course!). If you decrease your access points, you decrease the structures weaknesses. I could also do a barn door type, the bottom opening up separately from the top, allowing me to use it as a human door, a chicken door, and a way to look in on them without letting them out.
This would keep the chickens insulated and, I think, much safer than a structure with all four sides exposed. The only problem I might see with this is the possibility of insects getting inside. Not necessarily from the concrete side (although it's been known to provide very tiny pathways for insects) but on the ground-level wall.
I might also make the run extremely large and divide it up into two, either vertically or horizontally. I'd put a screen/wire/hardware cloth door between them and therefore have a way to alternate runs, allowing grass (maybe!) to grow or chickens to be kept seperate.
A personal modification I'd be sure to put in would be a separate fence, starting from the sides and wrapping around the hill and garden to keep free range chickens from ruining the beautiful roof (and therefore keeping the earth on the roof through the preservation of living plant roots).