I'll agree with the majority that, in your circumstances, no, you cannot just let them forage. I grew up on a farm in the hills of east Tennessee and we did just let ours forage. The only time we supplemented their food was when the ground was covered with snow. They certainly did not use 2 acres per chicken but we did have draft horses and cows in the winter so they did supplement their feed with grain from hay that those animals ate plus whatever they got from the manure. But as long as the ground was not covered with snow, they could find quite a bit in the winter. And we had plenty of eggs, not on the winter but during laying season. Not the 5 or 6 a week from each hen that is pretty normal for a lot of us on this forum if we chose our breeds for that, but still quite a bit.
I don't think you can just let them forage because your half acre is not all that big. They will wander further than that looking for varied food and get themselves in trouble, either getting your neighbors mad or possibly encountering predators. That road is also a real risk. Just because they are chickens does not mean they will win a game of chicken with a passing car. So, yes, if you let them roam, you will need a good fence.
Another reason they might have trouble living on just foraging is that they probably don't know how. I've found that chickens that I raise from babies in a brooder are just not that good at foraging. They rely quite a bit on the feed that I make available. Chickens that have been raised by a broody are much more capable of finding their own food. They still come by the feeder and help themselves to some easy pickings, but they sure do not depend on that feed as much.
What do chickens eat? I'll not get into too much on the prepared chicken feed. There are a lotof options out there for that. But from a foraging viewpoint, they eat a lot of plant matter. That can be grass, weeds, bush or small tree leaves, about anything they can get. It does not have to be green and living. They can be quite happy with brown, dried up plant matter. They eat seeds. This can be grass seeds, weed seeds, many fruits and berries. Grain certainly falls in this category. Most things you grow in the garden is fair game, both the plants and the vegetables. They eat creepy crawlies. They will eat about any insect or spider they can catch. I've seen them picking off ants. They love grasshoppers and crickets. They will catch and eat wasps and bees. They love worms, grubs, and caterpillars. If you give them a wasp's nest, they will probably tear it apart to get the larva. You will often see them scratching, especially in anything you have mulched. Not only are they looking for the creepy crawlies, they are looking for decaying plant matter. If they see an interesting morsel, alive or dead, they will eat it. Often, I see mine when taking a dust bath just eat dirt. They are getting some small sand and rocks to use as grit, but they are also just eating dirt. I think they get certain minerals that way. They eat meat. If they can catch a mouse, they will peck it to bits and eat it all. Mine especially love to do that with frogs. Some people cut open road kill and let them eat that. So what do chickens eat when foraging? About anything.
The fencing discussion is worth a thread of its own. There are a whole lot of options. What kind of fence you build depends on what you want that fence to do, mainly either keep the chickens in or keep predators out, but there are other considerations. I'll not go into that here.
So welcome to the forum. You might look in the Learning Center up at the top of this page and ask away on anything you don't understand. One thing I will warn you about. We all have different goals, circumstances, and experiences. There is seldom one right answer for anything that fits all of us. When you read something, try to understand the circumstances involved with that comment and take what applies to your situation. We give a lot of conflicting advice, partly because of our different goals and circumstances and partly because a lot of different things work. Keeping chickens does not have to be complicated. As long as you give them food, water, basic shelter from the weather and protection from predators, they should thrive. But keeping any animal does tie you down since they depend on you. I hope you decide to join us in the adventure.
