Sounds like clutch chatter in the limited slip clutches. If the gear lube is new or synthetic oil (85w-90), go to a GMC or Chevy dealers parts counter, ask for Limited Slip Diff Additive. It's about a 4 oz bottle. Add it to the diff, then go to a large parking lot. Make tight circles (right and left turns) or figure 8's for about 10 minutes.
The additive is a special lube that clings to the clutches, the tight turns help to "open up" the clutch pack to get the lube into the pack.
I know it sounds crazy, but it really works. GM has had many bulletins about rear diff noises and this fix. I think the tight turns works better than figure 8's, but I've seen it work both ways. Sometimes you need to perform it more than once. Mall or Supermarket parking lots on an early Sunday morning are ideal. D