Is he neutered? If not, that may be why he wants to get outside so badly. A chain link fence will not keep him from getting out.
It'll be much healthier for your cat to be indoors where it's safe from poisons, loose dogs, other cats, wild animals, malicious people... and so on (the list of dangers is quite long). Indoor cats live much longer, healthier lives than outdoor or indoor/outdoor cats and it's very possible to have a happy, well entertained indoor cat. It's also entirely possible to train a cat to walk on a harness/leash for safe outdoor trips. Read more on why indoor is better as well as how to make a safe outdoor enclosure for indoor cats:
http://www.littlebigcat.com/index.php?action=library&act=show&item=indoorsoroutdoors
http://www.geocities.com/heartland/pointe/9352/indoors.html
http://home.hiwaay.net/~keiper/indoors.htm
http://www.cat-world.com.au/cat-worldenclosures.htm
http://www.xmission.com/~emailbox/catrun.htm