A chuck assembly for use in a machine tool for holding a tool element comprises a chuck body having a sleeve integrally formed therewith so as to extend in the direction, which sleeve has a support bore defined therein for the receipt and support of the tool element and also has its outer peripheral surface tapered in a direction away from the chuck body, a fastening nut having its inner peripheral surface tapered in complemental relation to the outer peripheral surface of the sleeve and helically rotatably mounted on the sleeve through a plurality of roll bearings, and a reinforcing nut threadingly mounted on the fastening nut and adapted to be engaged under pressure with the chuck body when the fastening nut has been fastened and the reinforcing nut is then fastened.