A chuck for securing a working tool in a machine tool and including a one-piece, ring-shaped carrier member arranged outside of the end surface of the receiving end region of the chuck and parallel thereto and provided with cutting region having additional cutting elements distributed circumferentially around the receiving bore of the receiving end region and extending transverse to a plane defined by the ring-shaped carrier member and projecting away from the carrier member which secured by crews to the receiving end region of the chuck.