The rats here got through hardware cloth which is waaaay tinier than chickenwire. They didnt actually get in. They reached through, grabbed the birds (quail) and then pulled their heads down through/out through the hardware cloth and ate what they could pull through.
Rats can fit through spaces only one inch wide. For my pet rats, we use half inch wires for their cages. Definately pay for the good quality HW cloth. Be sure to nail it down tight, because they will test every boundry.
Well, or at least they'll try to, depends on how skinny they are. I found one this winter that tried to squeeze it's way through my 1"x2" mesh that I have for the chicken yard. Apparently, it got about halfway through, got stuck and froze to death.