How do I secure fleece to wire?

I don't want to sew it, because than I can't wash it. Do I just lay it on there? If I do, I have a feeling my chinchilla will just flip it over and he'll sit on the wires (like he did with his old fleece). I got him new fleece today and I want to make sure I do it right... how do you put fleece on (if you do) over your wire shelving in your cage?