Sounds like the rear end TSB issue. I just had mine replaced this past week and I will tell you it feels much better than it did even before the issue started. I'd take it to the dealer and bring in this:
Document ID# 1870450
Subject: Growl groan Shudder or bind from the rear differential when turning - keywords axle chatter cold G86 hot turn #PIP3911A - (11/03/2006)
Models: 2006-2007 Chevrolet Trailblazer SS Equipped with limited slip differential (RPO G86)
Condition/Concern: Same as Subject
Recommendation/Instructions:
Replace the rear differential center section (gear case) which will include clutch plates and springs with an updated spring rate. At the time of the release of this PI all parts in GMSPO stock have been purged and ordering the catalog listed part number will insure updated parts. Fill the differential by first installing 5.5 oz (163 mL) of Limited-Slip Axle Lubricant Additive (GM Part No. U.S. 1052358) then fill, 0.6 in. to 1.6 inches below the bottom of the filler plug hole using SAE 75W-90 Synthetic Axle Lubricant (p/n 12378261) meeting GM Spec 9986115.
Note 1: reference the latest version of tsb 06-04-20-003 for proper fluids and capacity.
Note 2: Synthetic Axle Lubricant, p/n 12378261 or p/n 89021677 each of these part numbers is the same axle lubricant, w/ differences in packaging only.
Please follow this diagnostic or repair process thoroughly and complete each step. If the condition exhibited is resolved w/o completing every step, the remaining steps do not need to be performed.
That's what I did and they found it was the exact problem. They ordered the rear end and put it in without any issues from the dealer.
