Jeff,
I am assuming the car has a 12-bolt rear.
What is the axle code on the housing?
Does the rear have C-clip eliminators?
The GM 12-bolt unit can be referred to as a posi or a limited slip unit. It equallizes the tire traction bias by using clutches inside the unit.
If your car has the original posi/limited slip unit in it, three possible things come to mind:
1) the clutches are possibly galled together or are badly "gummed"
2) the spider gears have galled to the cross shaft
3) the unit has had a HD clutch and spring set installed
(22 clutch plates and 800# springs)
Another possibility would be if someone installed a mini-spool at sometime in the past.
Pulling the cover is the best way to determine carrier type and also check if there are any problems causing the "hop" of the rear wheels.
If you decide to pull the cover, let me know and I can call and talk you through a few things to check/inspect while the rear is open.
Eric