Use galvanized welded wire or hardware cloth instead of chicken wire. Chicken wire can stretch and allow predators access to the run. If your windows and doors have traditional mesh screening, add a layer of hardware cloth to those openings to prevent predators from getting in the coop. The opening in the wire mesh shouldn't be larger than 1/2''X1/2''.
Bury galvanized wire underground to prevent burrowing predators. To do this, bury wire 6 inches underground, parallel to the walls of the coop and run. Then, bend the wire 90 degrees to run the wire out from the coop parallel to the ground for 12 inches. Finally, cover the wire with dirt. If a predator tries to dig under the coop or run, they hit the buried welded wire and stop digging.