Birds of prey are all federally protected. If you kill one and get caught there are stiff penalties. Best thing you can do is make your coop and run into Fort Knox for poultry. Protect them against the birds and other predators as well. Chickens are prey for everything--including but not limited to coyotes, your dogs or your neighbors dogs or the dogs someone else dumped on the road near you, racoons, possums, snakes, bobcats, lynx, bears, lions, etc. etc.
I take the too much is never enough approach--I like a little overkill. It helps me get lots of sleep at night. Start with 2" x 4" woven wire from the ground up to the top of your fence posts. Small mesh netting snug across the top of the run. Hardware cloth along the inside of the posts for the bottom 3 feet. And my personal favorite a strong energizer to put some zap in the electric offset HT smooth wire that are spaced all the way from near the ground to most of the way up the fence posts. Add to that another couple of feet of 2" x 4" woven wire attached to the base of your fence and laying on the ground outside the fence (under a light covering of dirt.) This will help deter K9 types from trying to tunnel under. And no simple latches on the gate or the door or pop door to your coop. Racoons are notorious latch openers. The electric should protect the gate to the run as well.
It will cost you a bit to set everything up but it will last many years.