It depends on the size of your run. If you have quail in there, chicken wire isn't going to be enough. You'll want it all to be 1/2" hardware cloth to keep the quail in and predators out.
Seriously, though, you're taking a pretty big risk by keeping a chicken in with your quail. It's likely...
This is not a good idea. Even if they are raised together and get along well, the chicken is likely to injure or kill some of your quail by accident just due to the size difference. Also, quail need to be kept enclosed at all times since they won't "come home" at night, and your chicken is not...