Hi XXXXXXXXX,
The most likely cause of this noise is a bad pinion bearing. One check that you can perform is to grab on to the yoke where the driveshaft hooks on the rear end and try to see if there is any movement at all. If you feel any movement at all, the bearing is bad.
Let me know if you are going to try and change it yourself. It may look easy to do, but there is a sensitive adjustment that is required. Also you should know that if this bearing is bad, it means that some pitting could have occurred and there could be metal filings inside of the rear end. Also when this bearing is bad, it could lead to other problems in the rear end like broken ring and pinion gears if it is not fixed.
Let me know if I can help you any further. (Go Pontiac!)
Thanks,
Vinny
ASE Certified Technician
33 Years of experience including ASE Master Tech 27 certifications, L1 Advanced Diagnosis