My '75 roadster 3:08 diff positrac did that while making a left turn. My shop replaced the fluid with new positrac gear lubricant.  It resolved the issue!

My friends '68 roadster 3:08 does the same!

Changing the diff fluid with a positrac lubricant may resolve your issue. 

Hope this is helpful!

I changed the fluid in mine. But only after a bunch of other preventative repairs. There was no drain hole in mine. So.. I drilled and taped the bottom. Total drain, flush with carb cleaner and kero. Put a flush plug in it. Filled with 80 oil and two pints of GM positrac fluid. Did about 10 minutes of figure 8s in a parking lot, good to go. No problems! 

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I think bad u-joints will make a chirping/squeaking noise when turning in a circle.  Don't think they clunk.

I towed a boat with my '78 and eventually they started chirping and got replaced.

If U joints made a clunk, they would be on the ground under the car. A quick peek would tell you if they were bad. Check all four for looseness or missing parts. They are not really hidden. 

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Every spring after the cars sat all winter this was an exercise that all would get before any serious driving took place - forward and reverse.  Was fortunate that no one ever called the local law enforcement kids for my doing "crazy stuff" in a parking lot...!!!

Jim Olson 

"The Toys"...!!!  Save the Wave!

Where I've been in a Corvette...!!!

Hey,  Yes its a dull thumping sound, almost like something is too tight and binding . 

I think a fluid change is the first port of call - inexpensive and relatively easy, with a small pump (no drain plug).

Depending on how long fluid has been there, change it regardless. I would have to hear it, or feel it. But, I think it's a worn or loose piece that transfers vibration to the body/frame through a rubber mount or suspension part. 

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My '75 was making a snapping noise in the rear end when turning.  I changed the diff fluid and added positrac fluid.  I forgot about this until this post and I realized it was not longer making that noise.

The first time I encountered this was after a 150 mile drive to Donnington Motor Circuit, in the UK, on a motorway (freeway).  As we turned into the circuit it sounded as though someone had taken a hammer to the rear end somewhere!  It was finer while we were going around corners, but after a while on a straight road it would bang again when we turned, although not as loudly as the first time!    I did the  the fluid change and the problem was cured.    

Given how expensive, and difficult to repair, some rear end issues are, a fluid change is a quick and cheap fix!👍

Wonderful! The easy route is the first route. Glad it worked out and problem had been rectified. 

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