Domestic "vegetarian-fed" chickens typically eat soy, wheat, and corn- grains high in omega-6 fatty acids, which they pass on to you.
Pastured domestic chickens get to forage for insects, but still almost always are fed a ration of soy/wheat/corn.
Poultry scientists are trying to solve the fatty acid balance problem. Unfortunately, one of the solutions, fish meal, is unsustainable and makes the end product taste well...fishy. Why rob our ocean's food chain, taking food away from delicious fish like salmon, to get some fishy tasting omelet? Beyond that, chickens didn't evolve to eat fish. That's the magic of grass-fed pastured beef- you get the benefits of eating an animal that is eating its own paleo diet.
Here is the kind of "chicken" our paleolithic ancestors might have eaten- a guinua fowl. What does it eat? "seeds, fruits, greens, snails, spiders, worms and insects, frogs, lizards, small snakes and small mammals." Look at all the meat in that diet! If you ever slaughter poultry, you'll notice they are basically a bunch of dinosaurs wearing fancy dresses. It might be possible to raise domesticated chickens "paleolithically" by also raising frogs, snails, and worms for their consumption and supplementing with a supplement mix that with a better fatty acid balance (flax, hemp, alfalfa, rice, quinoa).
Until I start my "paleo" poultry farm, I just will avoid making chicken a staple in my diet.
You could also hunt for your poultry. You know those Canadian Geese terrorizing the children in your local park? They are pretty tasty I've heard.