No its not a self centering one. There is nothing really in the way with the 3 jaw but their were a couple slots that were close to the jaw and I did not want to run the risk of the jaw falling in during a cut. You might also notice some shim stock on the 4 jaw that was to remove the run out. I measured the run out in 2 places at once with indicators and used .05MM shim stock to even it out. Maybe it would be better to say I made sure the axis of the body is first parallel with the shim stock then used the 4 jaw to make it collinear.