no chicken wire. By the way, nobody will guarantee the result except you. Because chicken wire is not an "approved" method. And skipping the chicken wise and using the mat as like kinda the same thing is like kinda the same situation. Sort of like that.
In some internet forums, people won't say anything except "here is the approved method". Anything else leads to never ending squabbles. Very few people have been in your situation. Choosing between chicken wire or mat or both. There are other "membranes" and other ways of getting thinset to stick to plywood, that are warranteed by the latex manufacturer.