A chucking apparatus for chucking an object contains a basic body which has a receiving space in which the object can be disposed. A chucking device is provided with a chucking nut which is screwable onto the basic body and by the chucking nut being screwed onto the basic body the object disposed in the receiving space can be chucked non-rotatably. The chucking nut has a plurality of roller bodies having a defined roller engagement structure. The roller bodies are held in an axially rotatable manner on a chucking body of the chucking nut and are arranged distributed in the circumferential direction on the chucking nut. The rollers by their roller engagement structure are in engagement with the basic body engagement structure of the basic body.