We have hardware cloth over our coop & run with an apron around the bottom so nothing can bother our chickens. Its worth it for peace of mind.We live beside a family with 3 dogs that would be more than happy to kill them if they could.They run loose all the time.
Your biggest threat is the mink farm up the road .They're serial killers that love digging tunnels.They'll kill the whole flock if they ever get inside. You need wire mesh with openings no larger than 1/2" to keep them out.(galvanized steel hardware cloth)