My woman has a little Boston Terrier that climbs a chain link fence with no difficulty, she likes to escape and harass cats down at the barn. When done, she climbs right back over to get to the house door. I have been tasked with putting an end to this behavior. My initial suggestion, to have one of her legs amputated, was rejected out-of-hand.
I'm thinking of hanging plywood strips, 1'x8' along the top inside edge of the fence, kinda like this:



By hanging loose I figure the critter cant help but get stopped by being trapped between the plywood and the fence.
I also thought about 6" PVC pipe fastened on the inside edge as well.
Or?
Thoughts and suggestions appreciated!

Our daughter "bought us" a springer spaniel some years ago and as a puppy, it would dig out under the dog fence we set up to contain it in our smallish back yard. I installed chicken wire at the bottom of the fence and bent it inward to discourage it digging under the fence. That worked. But it was not a climber. Your idea for a board at the top of the fence might work; you will have to try it and see.

You could run a low voltage hot wire about 3/4 of the way up. They sell the extension to extend the wire out so it wouldn't short out touching the metal. They have several strengths of the hot box so be sure to get a low shock one.