You should be able to. I plant my lettuce and spinach under my cucumber A-frame and they do fine there with only the dappled sun that comes through the vines.
Hmm, I wonder how the neighbor who watches our dog feels about chickens? He's over here morning and night when we're gone anyway to let the dog out and play with her a bit. We don't have any real predators in this area unless neighborhood cats count; we're in a small town and I thought for sure we'd have raccoon, deer, rabbits, etc. but they all seem to stay out in the cornfields where the food is easier to steal and there are less people & pets interrupting their foraging.
Here too. We have a big lot for our neighborhood at 1/4 acre, and we're actually considering buying the foreclosure next door to have more yard. Ours was the original house on the block and the man who built it held on to a nice yard for himself when he started splitting the property to build houses for his kids and grandkids. Around here, a lot of houses don't have much more than the space the house sits on. But it does come with perks - I basically don't drive from April through October because everything I need is walking distance from my house.