Four feet high MAY not be tall enough -- we clip our chickens' wings, and until we put up a higher barrier, we had one red star that would greet me at the back door in the morning -- none of the others ever got out, but . . . .
That said, she's older now (and thus heavier) and we're thinking about taking the top barrier down. We only stuck those green metal stakes in the yard and ran chicken wire around it for their little 'chicken yard.' The girls all peck at the door of their predator-proof pen (with the hen house in it) to get out in the morning, and then they all collect at the chicken yard gate to be allowed into the larger (mush more interesting, full of grass and lovely bugs) yard. They're allowed out in the backyard only when I'm home, since otherwise they'd undoubtedly destroy our gardens, etc., but we do let one of the dogs roam around freely when they're out there. We have trees in all the neighbors' yards, as well as in our own, and we know that we're taking a chance letting them stay out in the chicken yard, so it's still a gamble. They can go back in their pen whenever they want to, but of course a predator could also follow them back into the pen as well . . . .
One thing I'd suggest, from personal experience, is to make it very easy for YOU to get in and out of the chicken yard! We haven't been through a winter with the girls yet, but until we jury-rigged an easier system than we had at first it was simply a pain to go in, scoop the poop out of the pen's sand, water and feed, etc.
Sigh. It's still a gamble, though -- and if a hawk or an owl or something else does kill one, we'll probably rethink our 'open sky' policy. They all LOVE being free in the yard, though . . . .
So, I'd say that it depends on your particular circumstance -- good luck!