I wouldn't do that and I'll explain why. Chicken wire is great for keeping chickens in, but it doesn't keep predators out. Raccoons can reach up in that wire, and grab a leg, and they will literally rip your bird apart to get it out, and have their easy meal.
Not to mention mice, rats, snakes and things of that nature. A dog or fox could rip through that chicken wire.... And maybe a younger bird could get a foot through there.......So many things to think about.
This is just my humble opinion. I might be a bit of a worry wart. Both of my coops can be locked up at night so that nothing can get in there.