This noise is common to a number of high-performance cars with LSD. As said above, it is because of the different speeds the rear wheels are turning during slow tight turns. The diff includes a "clutch pack" on each side to allow for the slippage necessary to accommodate the differing wheel speeds. The slippage in the clutch pack is the source of the noise.
It was pretty universal on all C6 Z06s, and GM's solution was exactly the same as BMW's--installing an additive, driving slowly in circles, etc.. As others also said above, it does no harm to ignore it and do absolutely nothing. It is normal, and all the additive does is to quiet a harmless noise.