I've had modest success with hatching chicks under a broody hen.
Our first hen to go broody went when I was maybe 9 or 10. She was a leghorn, which is rare to see broody, and only hatched out one chick. Sadly, the whole family had been busy at the time to notice and we lost her to cats. We hadn't even known she went broody until 3 days before and had not expected anything to hatch so soon, or at all!
Then we got our "mother hen" as I call her. She's 25 ounces of pure maternal instinct, and bite. When we first got our chickens, it was because my mom thought they looked pretty as adults, and so, we did not know many of their breed names. I believe Mamma, and her boy toy, are both Mille Fleur d'Uccle bantams. She has gone broody sixteen times in her life, and she's only 4!
The first five, she didn't set for more than a week and a half or so, but she was setting. After that she went for the full three weeks, but only about 4 of the hatches have produced anything. Her first, had three chicks, Buff Orpingtons, but only two survived. Still pecking away to this day. Then there was a hatch that produced only one, rhode island red, so we bought a leghorn chick to be her friend. Sadly, a dog took them both out a few months ago
Then there was one setting that produced three polish chicks that we had gotten from our neighbor. All three are females and all brown, and they are doing just fine. Then, there is her final one so far, which happened a bit ago. We decided that we wanted more Bantams, so we let her set on her own. There were only six eggs, and only 2 hatched out, but they are a spitting image of their parents. A pure bred male and female Mille Fleur d'Uccle. It turns out, the male is from an egg we got from our neighbors, but he looks just like the "father".
Now those two are a breeding pare, and about four days ago,her daughter started setting. It's in the coop in a basket that's hanging from a pole. She's doing fine and we will move when she's a bit farther along, as it has worked in the past. She is setting on 18 eggs! each one tiny, being a Bantam and all, but 18 is a lot. I have made an incubator and preparing to fire it up if she can't handle them, but honestly, she seems to be doing fine. When I check the eggs all are warm and underneath her, somehow. I candled at day three and it looked like at least 14 or more had spider veins, so cross our fingers. 
About 8 months ago, I begged, I mean begged 
for my mom to let me get some Silkies. They have and will always be one of my most favorite breeds. Now since, I have a hard time sexing Silkies, because of their fur-like feathers rather than feathers, I didn't notice that we got a boy and a girl, but boy am I happy. She began to set a few weeks ago and hatching day started last week. Now I say started because there have been a lot of factors with the eggs while she was broody. So she hatched out her first one last Sunday. Then Monday she hatched another, and another one the next day. Sadly, the first two didn't make, and just laid down to die. But her third one, which was a Silkie like herself, is flourishing now, being about 4 days old or so. So far she has hatched out one a day for the past week or so, and we still have four eggs to go. Six are out and about now, four are white and what I believe to be Sultan chicks, 1 male 3 female, and 2 are Silkie chicks, 1 male 1 female. I'm not sure what the other four will come to be, but she is still trying to hatch them out.
I'm hoping that the rest hatch and that our Bantam hatches out her little ones. Now that I have plenty of incubators, and soon, plenty of chicks. I think I might start selling the pure-bred fertilized eggs and chicks. I have done as much research on chickens as I do on all my book reports for English, and I have a 102, so I guess that means a lot. My only issue is with sicknesses.
I've noticed we have a few breeding pairs. The Sultan and his sultanah, the two pairs of Bantam couples, the Silkie couple, the three Polish females and their male, and the Guinea hens and mate. Our others include, another white Polish female, a Buff, a Ameraucana leghorn mix, a Silkie male, and a Silver-Laced Wyandotte. We have some great chickens, and will hopefully hatch out some great chicks. Hopefully I sexed them right, the feathers can be hard to read sometimes.
