I cannot imagine a device that would keep climbing predators out, that would not also bar the chickens from entry.
However, one idea comes to mind. One could take advantage of the fact that all predators have muscle structure that conducts electricity. But birds' legs are dry, without moist muscle structure, and do not conduct electricity well at all. Now, mind you, this is not the reason birds can sit on electric lines; they do that because they are not grounded. But, electric bird netting takes advantage of the dry-leg structure in this way: It is designed so that the electricity affects invading predators, not the chickens. A predator on the ground touching the electric netting gets a shock. But a bird on the ground that also touches the netting feels nothing...because of the dry legs that don't conduct the electricity at the power level that is present in an electric fence energizer.
Now, take into account also the movements of the chicken and the predator. A chicken hops from perch to perch, while a predator clings, grabs and climbs a ladderlike structure.
So, one could devise a ladderlike structure that gives chickens a clear, easy path of entry. The rungs could be insulated from the rails, with the positive side of the energizer attached to the rails, and the negative side to the rungs. Better yet, make every other rung positive/negative, and have the rungs too far apart for a chicken to walk, forcing it to jump from rung to rung.
A chicken hopping from rung to run would never touch both positive and negative, and when they did in fact have one leg on the rail and one on a rung, their dry legs would protect the chicken from a shock.
But a predator climbing the ladder would have a nearly 100% likelihood of at one time or another touching both a rail and a rung, or consecutive rungs, depending on how you set it up, thereby getting shocked.
Such a set up should present a nearly 100% effective predator barrier, but an equally effective opening for chickens to have clear entry. The only animal I can think of that would eventually solve the problem would be a squirrel, but since they are not predatory to chickens or eggs, to my knowledge, that should be a moot issue.
