If you've read a lot of posts on the subject, then surely you've noticed that chicken wire is the MOST commonly breached type of wire when someone is lamenting that XYZ predator got into their coop. There was one one here already today where someones own dogs ripped through chicken wire like butter.
Chicken wire is good to keep chickens in, not predators out.
So, if you want to keep predators out, choose another type of wire for your run.
Hardware cloth is good for ground level, or to super protect chickens from small paw-ed animals like racoons and possum from grabbing through the wire - use it for sure near anywhere they will be sleeping to prevent this problem, or where you will have baby chicks out.
2"x3" welded fencing is pretty good, cheaper wire to use for large runs where dogs/foxes/coyotes are a problem.
And don't forget to cover the run for maximum protection to keep away the birds of prey.