You can get pastured chickens, but they're local, seasonal, and in limited supply. For me, since pastured chicken is not available now, I buy Springer Mountain Farms (because they're in GA). Bell and Evans are also good. These are humanely raised, cage free, free range, vegetarian fed, no hormone, no antibiotic chicken. It's the best you'll find outside of a local farm.
Most Paleo folk are a bit down on poultry - it doesn't have the same coveted O6:O3 ratio as large mammals like cattle, pigs, elk, bison, etc.
But I like the simplicity of cooking, and the variety in diet. Since we eat plenty of fish, I'm not too worried about the amount of chicken we eat.
Here's a good article on chicken labeling, and what to look for: http://www.marksdailyapple.com/chicken-labels/
Our chickens love fresh grass, grain, kitchen scraps gallor, bugs, meal worms...it's a real pleasure watching them digging up everything. They have totally denuded our backyard so this summer I am hoping to create a system of grass regrowth to keep them in fresh grass at all times. I'm wanting to replant with hopefully non-gmo feed grasses rather than lawn grasses. It will be an experiment anyways. We have a large organic, Paleo family so there are lots of good scraps for them. The biggest challenge I have is finding non-gmo corn scratch for them primarily during winter months. They need it to maintain body heat. My chickens hate the organic scratch available as it has no corn and very little grain that they like in it. Because of their refusal to eat it, I had to go back to buying them the standard corn which I hate but they were suffering. I have a new plan of attack for next winter though. Chickens are amazing creatures. They need meat (bugs/worms) and lots of greens plus grains.
It's hard to grow pasteured chickens because in many places the coyotes, wolves, bob cats, and mountain lions will eat them if they are not enclosed. We keep ours in big pens and feed them grass, kitchen scrap leftovers, and grain. Birds are designed to eat a lot of grain so it's not bad for them like it is for cows. But they should also have other things like fresh grass and insects when possible. A chicken needs protein/meat for best health.
In the wild, red junglefowl, which all chickens are believed to come from, are omniverous and eat lots of insects, especially ants and termites, as well as invertebrates and seeds. (they didn't mention grass for the wild ones but I would not be surprised if they eat that too)
Also, many chickens have soy in their feed, even when they are organically fed. It is tough to find good fed chickens. My local farmer buys organic feed, but he said because he is so small, he can't get it without soy. They are free range though and it helps. The eggs are the darkest orange eggs that I have ever seen.
Tropical Traditions sells eggs from chickens that are soy-free and given a feed based on coconut, with I believe, some mega 3 supplements. Not natural but perhaps a healthy egg if you can't source pastured raised chicken eggs near you.