Baron is right. If you are not clipping their wings, then 6 feet high is a minimum. 
Chickens are not great flyers, per se. Not like hawks or crows. And much is breed dependent - the larger heavies dont fly as well as the lighter breeds.
But they can manage some fairly surprising hopping flights over short distances. They are bred from jungle fowl and so are able to get up into low branches. Plus, there is always at least one that is extra energetic and seems to be unstoppable.
If your goal is to keep them confined without top netting, then wing clipping is the best answer.
Another option on pred control is to extend the fence wire out away from the main fence, parallel to the ground and just buried below it. Then when digging preds hit the wire, they are (hopefully) deterred.
And dont forget the Joy of Electric Wire.