There are two approaches I know of:
The most reliable is to put up a conventional (artificial)
fence, but grow things up it. We already have a passionfruit growing on more conventional chook wire fence, and it is in serious risk of pulling the whole thing down. For the latest extension we've erected weldmesh panels, 4mm (1/6in?) wire and 4inch square holes, with bamboo posts. The fence panels are seriously over engineered for keeping chooks in, but
should be strong enough so we can grow heavy climbers (Choko, Chili Cayote, Children...?) on them without worrying. Looking at it now, and the lack of any lions locally, maybe 2mm wire would have been enough!
The other thing we are trying is a true living fence, using Bana grass. This is a 6ft clumping grass, apparently a sterile hybrid, but very fast growing and is very dense at the base. It's not quite ready yet, and will probably need some enhancement at the base in the first couple of years to stop chooks pushing through. In the winter I have thinned it out, cutting about 2/3rds of the culms (canes/stalks) down to about 2ft high. This lets more light through, but should still prevent flying over. We'll find out how it goes.
I suggest you need aim for 3 things:
1: Really solid at the base to prevent chooks pushing through (fencing may be necessary). The smaller of my australorp crosses pushes through a 4in wide, 8in tall hole. So 2in wide, or 4in squares should do the trick.
2: Pretty dense for at least 2ft (to be experimented with!) to prevent the birds doing a "power assisted hop" on to the top of any fence (I'm guessing 4in wide gaps would be enough)
3: Flight deterrent up to the full height (I need about 4ft). This just needs to be something unstable, possible solid looking that the chicken won't trust themselves to launch themselves at in flight
If you're happy to have the occasional escape, you can have some fun. The benefit of bana grass (and some other grasses/bamboos including sugar cane) is you can take a single culm and bury it horizontally, it should sprout at each leaf node along the length, giving you instant (in 6 months) hedge. I put down 3-4 culms to try and ensure it is dense enough. Depending on how many chicken you have for the area, you probably want to exclude them completely from getting to living parts of the fence until you think it is dense enough at the base to withstand them. Have fun, let us know how it goes.
