It sounds like you haven't broken it in properly, or at all. Clutch type LSDs will chatter at low speed until they are broken in, and are still a little chattery until all of the clutch plates mate properly. You could probably find break-in instructions (repetitive figure 8s usually) on one of the LSD manufacturer's sites, or on KAAZs site.

And don't use synthetic fluid, it lubricates too well and won't allow proper clutch plate mating...

KAAZ LSDs are nice, make sure you treat it well..