I believe the answer is a personal decision. Some will tell you that the chemicals will leach out into the soil and the birds won't be organic. Others may say that non-pressure treated lumber will rot.
It is really your choice.
My personal coop is Pressure treated - because I want it to last with as little maintenance as possible.
I have pressure treated on anything that will touch the ground. The rest is regular construction lumber. We originally (or rather, DH originally..) built the coop as a playhouse for our children, and we didn't want them to be in contact a lot with the pressure treated lumber. Even if the coop was pressure treated, just use regular 2x4 for roosts, where they spend most of their time. If you have shavings on top of the flooring, they really won't even have contact w/the chemicals there.
New to this forum but have had chickens for 3 years and have now built a bigger better brand new coop and added 6 new chicks to the flock. The first coop we built we used all regular untreated lumber. We used cedar for the part that touched the ground and painted with so called barn and fence outdoor paint the entire coop and run with 2 coats. It was the small coop that looks like a playhouse. Anyway, we just moved the entire coop/run to my friends house who wanted our old coop. It was badly rotted along the entire bottom and almost came apart and had to try and reinforce it the best we could. This time everything we did was pressure treated to last. Painted it with quality exterior paint. Inside the coop I used double layer of 6 mil plastic sheeting and stapled it up about 4 in. up the wall all the way around and added sand which I LOVE so much better then shavings. For the run we used 8ft pressure treated landscape timbers about 8-10 ft apart and pressure treated 2x4's for the gate. We attached 2 ft high 1/2 inch galvinzed wire along the bottom and 4 ft of 2x4 galvinized garden fence above the 1/2 inch. The run is sand as well. I am so much happier and know that this will last for much longer. I really am not afraid of the treated lumber hurting the hens or their eggs.
Check this page out. It has some good info about pressure treated lumber.
Short answer: about 10 years ago the lumber industry stopped using an arsenic containing compound (CCA) and went to something else, even though the hazards of CCA were minimal.
The biggest risk for CCA leachout was for submerged lumber: boat docks in small lakes with minimal water flow.
Use PT lumber for ground contact. Personally, I hate nailing the stuff, and minimize my use of it for that reason alone. It's hard as heck and tends to split weirdly.
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If you make a pilot hole the nails tend to go in much easier!! I do that with my landacape timbers because the nails are the 6" twisted kind!! Pain in the butt if you don't!!
I wouldn't build anything that was touching the ground with anything but pressure treated wood!!