You may want to look for tracks (foot prints), look at how they are getting in too. Was it through digging under, going over, going through fencing. Size of the hole they made? Was it in the day or night? Are your chickens locked inside a secure coop at night? Many factors here, but that should get you into the investigative mode. Good luck, let us know what you find out! You may also want to set a live animal trap and see what you catch!
Most predators can climb very well, especially coons and possums. Owls can fly in...
Last year I lost about a dozen full-grown pullets and cockerels to a skunk. Finally saw him and shot him. I new it was him because he'd leave his smell around the coop, and he was the glossiest fattest skunk you ever saw.
I haven't lost a chicken since we shot him. He'd kill them, and then take them under the coop to eat them (found that out the following spring when I looked under the coop for eggs
An ounce of prevention is worth a pound of cure! I have a top over their run and also put up electric fence around the outside of the run and fenced in area that they have! Mine have a 14 x14 run with a top that they go in at dusk and the gate is closed even though the entire fenced in area is has hot wire! I set my hotwire at 6 inches 12 inches and 18 inches around the run and the house! This not only prevents the diggers but the climbers! Small fence chargers and elec wire are cheap and very effective against preadators and the top keeps the owls out at night! they go in at dusk with a head count and then the gate shuts and when the sun comes up are allowed to run free! Your problem sounds like a Fox climbing the fence if your finding feathers off in the distance BUT the Fence does work