I have a 12X12 dog kennel I house our chickens in (their coop is inside of it as well) and we have the entire thing ran with chicken wire across the top, sides and gate with hardwire around the bottom 1.5 feet. We used plastic ties to secure sections together for the roof portion as well as securing the wire to the chain link - over the roof, we do have it "tented" with a "T" made of wood, secured to their coop roof to pop up the wire and the tarp that covers the entire kennel. This prevents any water and/or snow from getting inside the pen and collapsing. With the snow, we just go out and brush it off (anything over 2 inches) with a broom.
No issues yet and we have a pair of nesting red tail hawks in our back yard - and yesterday I saw a bald eagle flying around our property as well.
So long as you support the wire, you'll be okay. Plastic deer netting - I wouldnt use personally - something can get right through that by chewing faster than it can chicken wire, not to mention there is no structural support with it.