Thinking it over, I wonder if it is because I live somewhat near the airport, I suppose chicken instincts aren't developed to know the difference between planes and other big birds. I've never seen any large birds that would pose a threat.
I hear stories of other people's chickens wandering off or flying over fences, or free ranging over acreage, but mine are never more than 20 ft from their coop! At least I don't have to worry about them getting lost.
Ironically the only danger they have ever encountered was from my own dog, who managed to get in their brooder when they were a few weeks old and lick them half to death! They survived obviously (they weren't actually hurt, just wet and freaked out), and don't really seem to pay her any attention especially. She is not out when they are out, but she barks at them through the glass door or occasionally charges their coop, and they just blow her off, lol.