Hm, I don't know about keeping them in a cage, it might work.
I'd imagine loose ones could keep out of the way of chickens for the most part, you can get them in bulk and cheap from most reptile breeders.
Like said above, all the lizards will die unless they get access to unfiltered sunlight, as well as if youre not in an area theyre native too they wont survive without you maintaining the proper temps and humidity, not a good idea at all.
If you're looking for a creature to control the flying insect population in dark cool areas spiders are a much better option.
my "coop" is a 12x20 barn style shed and here in maryland its warm and humid as we speak. I have the impression that I've caused some folks to worry. I am a animal lover and have had anoles a long time ago, would not want to put their little lives in jepardy. I have heat rocks, special vita-lights etc. for keeping anoles inside and was just entertaining the idea of making a little outdoor cage for the daytime....
Never meant you werent, was just saying that unless you live somewhere where they're native they wont do well outside especially with no acess to sunlight, and personally I love the idea of a barn with a bunch of big spiders.