Hi Carrie,
A big welcome to the world of chinchillas, your going to have a blast for years to come

My cages are made with 1/4 mesh, not much gets out,but I do cut cardboard and fit around. They can't get their teeth through to chew.
I have also used pexie glass pieces, screwed on with pine blocks inside the cage.
Gives them a little something attached to chew also.
Put pine around even inside, and just replace it when they chew it up. Should take them a spell.

I just keep looking until I find things that will work, you'll need a good imagination with chins in your life.
