I'd be very careful about shooting anything at a Great Horned owl that could kill it (like a pellet gun) - they are protected. How secure is your coop? Do you have an enclosed run? Do your chickens go in at night? Some solutions - Make sure they're in the coop well before dusk and don't let them out too early in the day. Beef up your run. Beef up your coop. There is always some risk to free ranging (if you're doing that). If they're safely in a coop and run, they should be fine.
It is forever more illegal and a Federal Crime to shoot any owl, that is unless you are a member of the US Forest Service in which case certain members of the Forest Service get paid to go forth and shoot Barred Owls all day long. It seems that our friends at the Forrest Service discovered that cutting down trees
was not what was killing off the Spotted Owl but rather the Spotted Owls were interbreeding (or is it outer-beeding) with Barred Owls. Even the Forrest Service employees have a hard time telling the difference between an endangered Spotted Owl and a non-endangered Barred Ow so it is a fair question to ask them how many endangered Spotted Owls have they killed by mistake. The saying in the Spotted Owl community is "Once you go out with a Barred Owl you'll never go back to a Spotted Owl
Oh the Feds have a song and dance about how the bigger, stronger, more aggressive barred owl is killing off the
smaller, weaker, less aggressive Spotted Owl but it is all BS because no one wants to own up to destroying the lives, families and fortunes of the forest workers in the Pacific North West who lost their homes, businesses, and lifesavings because of incompetent environmentalist.
Now if you were an Alaskan Native you are or at least you were allowed to trap and kill owls. The reason being so they could enjoy Kentucky Fried Hoot Owl for Sunday Dinner.
Speaking of trapping, don't ever set a small foot hold trap on the top of a wooden fence post and attach the chain to the top of the post. It is a Federal crime to startle an owl. It is also illegal to erect a tall pole (oh say 10 foot or so above the ground, run a hot wire up one side and across the top and a parallel ground wire across the top and down the other side then attach the first or hot wire to your electric fence charger. This is guaranteed to cause any owl that closes the circuit to forget about chickens and force it to eat rats and mice.OH the horror of it, forcing an owl to eat rodents. What's this world coming to?
I met an old Cajun once who told me that Great Horned Owl taste just like chicken. I believe him because in my experience a Great Horned Owl family will kill between 4 to 10 chickens a week if they need and want them and have access to your flock, and owls taste like what they eat.