A little clarification first. Trucks do not use limited slip differentials so you are not going to find one. Those are used in cars, trucks use a Eaton G80 LOCKING differential.
Yes its possible but you can no longer buy the new case assembly from GM parts. Find out what your ratio is and go shopping the salvage yards. If you can do the work yourself it would be a lot easier to buy a complete rear axle assembly and replace the complete unit. To install just the center Locking differential portion is not a easy do-it-yourself job as it requires special tools and skill to set it up. It my seem to cost a lot more to buy a complete assembly but if you just get the case (the locker) portion and then have to pay someone up to 8hrs of install time you won't be saving much $, + when you change the center case you will have to install new bearings and or other parts depending on the wear in your differential. Just a lot easier to replace the complete unit and often the salvage yards will buy your old unit from you or charge you a core and credit when you return your old one.
4x4's require the the rear axle match the front axle in ratio or else you are going to have problems in 4x4 with different ratio axle so if you change ratio, you need to change the front to match.
Nevertheless, its going to cost you some money to do this. The parts are not cheap, either new or used so budget up to $1000 to get this done as locking differentials command a good price and are few and far between so the yards will ask a premium price. It may cost you much less but it could also cost you more. There is just no sure way to put a precise estimate on the cost due to so many variables.
Then there is the after-market, you can get them for a wide range of prices but then you need to find someone who will/can install them for you. I still think though that finding a complete used axle assembly would be the less cost alternative. unit guaranteed or $400 as is.
Here is a vid explaining the difference between Limited slip and Locker
http://www.youtube.com/watch?v=k5DPoXWxDfk&NR=1