Well I posted over in the Z06 section and only had one reply back about a similar issue.
I brought my car back to the dealer for a strange problem with the clutch. When you first start the car, put it in gear and let out the clutch it almost feels like the clutch is chattering. You actually have to keep the RPM's above 1200 to keep the car from feeling like it is going to stumble and die.
If you put the car in neutral, let out the clutch, push the clutch back in, place it in gear and go there is no chatter from the clutch. With this method you can ease the clutch out without any additional RPM. The clutch felt like this from the day I picked it up but I just thought it was inherent to the Z06. The mechanic was on the phone with a GM tech for quite a while trying to figure this one out. The GM tech told the dealer to change the clutch fluid and bleed it. The Mechanic said GM had a few similar problems and changing the fluid and bleeding the clutch took care of it.

The Mechanic tried the flush and bleed with the same results. GM authorized them to change the flywheel, clutch pressure plate and the slave cylinder. The parts should be here next week and I hope this will take care of the problem. The car only has 3300 miles on it with no track or strip time.

Has anyone else had a problem like this with the clutch?? Is there a TSB out on this?

Thanks

 

I had the same problem and i changed the stock fluid with Royal Purple MAX GEAR sae 75w-90 with one bottle of the GM ADDITIVE and i haven`t had the problem since. Change at 2400 miles and now have 5000 miles and no more noise. When you change the fluid go to an empty parking lot and do a bunch of figure 8`s and circles in both directions and that will solve your problem