When I gun it on 1st, 2nd, or 3rd, it sounds as if the wheels are slipping. I hear a chirp on the low end of the torque. Could it be that my LSD is faulty? Thanks.

 

Get someone to watch from outside the car, or lean out of the windows. What surface are you driving on? You'd need a lot of ooopmh to chirp the tyres in 3rd gear on tarmac.

If the LSD was playing up, it would probably make a horrible grinding sound. I wonder if it's engine related. You're in the US, is it a turbo or N/A?