I've just done this and it was really fun - though you have to figure out what to do with the boys.
It's best to get fertile eggs from a local breeder or chicken-keeper, if you can - check your local craigslist. People will ship eggs, but shipped eggs often get mistreated by the post office, or get all jiggled up, and you don't get a good hatch rate.
I drove a couple hours to get a special breed of fertile eggs, 3 hours back including stopping for lunch, gas, etc. I got a dozen eggs, thinking conservatively, and 10 hatched! 2 were not very healthy chicks, but 8 were.
Broody-raised chicks are known to be healthier and more disease-resistant. And it's totally wonderful to see their sibling bonding and mommy bonding.
You should check one of the two long broody threads to get an idea of some issues:
1) Will your broody be a good broody? She might lose interest early on....some attack the chicks! Many are wonderful mommies.
2) Whether to separate the broody and eggs/chicks from the flock, and how to integrate back.