The chuck (10) is comprised of a chuck body (11) having an inner cone surface and a grip head (12) with a corresponding outer cone surface. The grip head (12) is subdivided into individual clamping jaws (21) by several seperating slots, said clamping jaws being connected to the grip head (12) by means of elastic connecting elements (22). Recesses (25) are provided on the inner cone surface of the chuck body (11) at least in the peripheral area of each seperating slot of the grip head (12), preferably also in the peripheral area of the apex line of each clamping jaw (21). Said recesses (25) have peripheral extension which is greater than that of the separating slots of the grip head (12) or the apex region of the clamping jaws (21). The axial extension of the recesses (25) is at least identical to the largest overlap area of both cone surfaces. The recesses (25) are filled with a filling body (27), made of an elastic, compressible material, up to the imaginary inner cone surface. The filling bodies (27) are permanently connected to the chuck body (11).