When a new mechanical LSD is installed, it can give out an unusual chattering noise. This is caused by the clutch plates vibrating as they slip over one another and can be reduced or eliminated by proper break-in of the LSD You are most likely to hear it when driving at low speed or backing into the garage. Once the LSD, has been properly broken in the noise will disappear, although some larger LSD,s can continue to make some chattering noise even after break in.
The other common cause of chattering from your LSD is using the wrong oil. Both poor quality oils and all-synthetic oils can cause chattering.