cockroach problem near chickens

[blafo]

We got our first 4 backyard chickens 6 months ago and love them. We placed their relatively small coop adjacent to our garden shed, which makes a nice solid shade barrier of the shed, a Japanese weeping plum tree, the fence and the coop in our 100+ degree central valley ca weather. Problem is that the shed sits on wood beams placed on a concrete surface, which gives it a small underneath crawl space that turns out to be an ideal breeding ground for cockroaches. Add to that the food spilled from the chickens' feeder only a few inches away which is a feast for the roaches at night. We are not worried about the cockroaches vis a vis the hens since one is nocturnal and the other diurnal, so they never see each other. And the ladies would probably just gobble them up anyway. However the cockroach haven we believe is the source of roaches infiltrating our garage and house. We would like to annihilate them but are concerned about pesticides, even if they are out of reach of the hens, somehow making them sick.
I read that boric acid applied properly is effective against roaches and less toxic to humans and pets than other pest chemicals. My question is, if I treat underneath the shed with boric acid and cockroaches get in it and move out into the hens' area before dying, and a chicken eats one, how concerned should about how that will affect the chicken?

 

[ChickenCanoe]

I wouldn't be too concerned. The roaches only come out at night when the chickens are sleeping - which is why you still have roaches.

 

[carlf]

Cockroaches are everywhere outside, not just under your coop.
If you are concerned about them getting into the house, place boric acid, bait and/or use a perimeter spray around the house.