You may know that the ideal plant might not exist, in that it might not cover the fence at all times of the year, but I think your best bet would be a native (can usually take all weather conditions) that is also a vine. Here is a link to such plants for Oklahoma http://www.ehow.com/list_7190473_native-oklahoma-vining-plants.html
Here's another site for best hedges for oklahoma, you will want something evergreen and hopefully native
http://www.gardenguides.com/110375-hedges-plant-oklahoma.html

Thank you louisianagal! I really like the evergreen Wisteria :)

CAUTION ON WISTERIA It is my understanding that there are several varieties of wisteria. Here in the south some of them get HUGE and will pull down a chain link fence or large arbor or pergola. Do some research first in case that is one that will become a monster. And believe me they do.

Have you considered Carolina Jessamine or Coral Honeysuckle? Both do well on a chain link. I once bought two bare root coral honeysuckle plants on ebay for next to nothing and in two years my chain link was covered.

I echo the comment on the wisteria. I wouldn't risk a wisteria on a chain link ...

Can't say how they'd do there, but also explore Bignonia. some of them are pretty tough, but not necessarily malicious.