Ok, here's the thing. I've got a broody hen sitting on six white Leghorn eggs. They're due to hatch in two weeks. They might not hatch, but they probably will--and I will have six adorable fluffy little yellow escape artists.
I already have one Leghorn hen; she's a brilliant egg layer, but also brilliant at getting over nearly every fence lower than 2 m. My chickens for the most part coexist peacefully with my kitchen garden--except her (I still haven't forgiven her for the leeks). I use the basic paddock shift method outlined by Paul, although my hens have a coop and run at the back of my very small suburban property. They get moved to a new section of lawn or beds every week, but have permanent access to coop and run.
I'm chasing after the Leghorn most days; sometimes multiple times a day. I can't tell you how many times I've nearly wrung her neck; the only thing that's stopped me is her amazing eggs. Why did I say yes to more Leghorn eggs, generously given to me for free by a colleague? Because they were free, I didn't have to search them out, arrange a meeting time, pay postage...whatever. But mainly because of the eggs, those reliable, beautiful daily eggs, even in winter. We wouldn't have had eggs last winter if it weren't for Leghorn Florry, despite the fact that she's two and a half.
Anyway. To get to the point.
Here's a fence treatment that I have done, and it works. They need to be 1-2 inches apart, or Florry just jumps up and shoulders between them. That's Rock behind them, incidently. I'm collecting straight-ish garden trimmings as fast as possible, to cover the chicken wire currently enclosing the veg patch. It's a long piece of chicken wire, and I've only got about 1/5 of it done. I've got another two or three months before judgement day, and by then, the main summer garden will be over, so hopefully damage will be limited anyway.
I hope these new chicks aren't all boys...