Abstract: For selective outside or inside chucking of a workpiece on a lathe use is made of a base unit split to provide a set of three or more holding segments capable of being either contracted for grasping the exterior of a workpiece or spread for grasping the interior of a workpiece. There is a set of jaws complementary with respect to the segments and designed to accommodate a workpiece of selected size. Each individual jaw in turn is mounted on one of the holding segments with an attachment permitting removal of the jaw for replacement with one of the jaws of a different set for holding a workpiece of different size.