First off, it depends on what kind of chicken you have...
The broodiness is often bred out of "commercial" egg-layer breeds, because it inhibits them from going broody (which stops them from producing eggs for the time being while they set).
There are broody breeds like the above mentioned, but I know that silkies, bantams, brahmas, etc. get broody. You'll have to figure ask around to see if anyone knows anymore broody breeds (or do research).
Also, lol, my broody hens will lay eggs until they have up to a certain amount and then they will set and hatch...
Do you have a rooster? It sounds silly, but I know some people who try to hatch eggs from hens that have never been around a rooster and those eggs won't hatch, because they haven't been fertilized. Unless you are trying to hatch eggs that are sold to you (we're thinking about doing that since one of our hens are broody now).