Thanks for all the good advice. I did try using fishing line across the top of the 6' chain link fence that is my run. (2500' of line at 6" intervals back and forth over 40'x15' run)
The next day there were loose strains of line and a dead, picked over chicken outside the fence. So much for THAT internet advice.
I plan to enclose a portion of the run but am concerned they won't have enough area to graze if I confine them to that area.
Does anyone use natural shrubbery or 'hides' for their chickens in open runs with success? I expect the answer is still "build a complete roof".