As for your question, I do not keep moniters because I cannot properly house them at this time. But I do keep a green iguana and I know she can rip apart chicken wire when she choose too. We once had to seal up a hole in her old cage (she was about a full foot smaller than she is now) with chicken wire temporarily. She had it opened like a tin can within an hour.
I doubt moniters, which I think are much stronger, would stay behind chicken wire for long. Then you have a potential risk to your neighbors and whoever else, not to mention losing your moniters. Also the moniters could be really scratched up by rough chicken wire.