We have various birds of prey where I live, and I felt the same as you when I first got my girls. Initially I covered a large run with netting for them, as I was so worried that something would swoop down and attack them. However I also let them out for supervised free ranging, and it got to the stage that when they were confined in the run they got a bit miffed - they could see all the wonderful things that they knew about on the other side of the fence, and wanted to get out there and scratch, peck, chase and eat everything they could!
Then when I watched them free ranging I realised that I was probably worrying about them a bit too much. There are plenty of places for a chicken to hide in my garden - in bushes, under a trailer and a under a very large terrace. At first when they heard the alarm call of the wild birds (I have a feeder in my garden, so there are lots of wild birds around), they would immediately run and hide. Then I noticed that they were starting to notice the birds of prey themselves, and would sound their own alarm call as they went and hid. As you have a rooster, he will quite possibly be the first to notice predators and alert the flock (that's part of the job description for roosters!) He may also sacrifice himself to protect the hens if a predator strikes - again just doing what nature programmed him to do.
Because my girls seemed quite aware of predators, I started to let them free range when I left the house for a couple of hours, then I did it for a whole afternoon, and finally for the whole day. They now free range all day every day, and the covered run is only used for isolating individual birds for health / behaviour reasons. Obviously I run out and check on everyone the instant that I get home - I haven't stopped worrying about them completely - but I feel certain that they are not the sitting targets that I initially thought they would be.
The result of this is that they are very happy with the fact that they can free range all day, I get a lot less pests in my garden, and I also buy less feed as they find so much else to eat (they have free access to oyster shell to make certain they have enough calcium for the lovely eggs they give me).
I'm not saying that there is no risk - in any free ranging situation there will always be a predator risk, no matter where you are, or what time of day. The thing is that you have to balance the desire to free range your girls (and their desire to be free ranged!) against the possible risks. The birds of prey round here are not huge, so they tend to go for the finches, sparrows etc (although I have seen one attack and kill a blackbird), and I don't know if the fact that my girls are so much larger than the wild birds puts them off. Having said that, I have raised a dozen day old chicks at various times, all free ranging from day one with a broody mother hen, and never lost a chick to a hawk attack.
At the end of the day it is a personal choice, and one that you have to live with. If I do ever lose a chicken to a predator then I will obviously be upset, but I will also know that up until that point she had an excellent free ranging life, and that I didn't deprive her of her freedom and the chance to be a real foraging bird. Whatever you decide will be right for you.
