A motorized surgical handpiece with a chuck. Internal to the chuck are clamping members that releasably hold clamp the shaft of a cutting accessory to a drive shaft so the cutting accessory rotates upon the actuation of the motor. The chuck includes a collar with an opening through which the cutting accessory is inserted. The opening is non-circular in shape. When an accessory shaft with a cross sectional shape that matches the shape of the opening is inserted in the opening, the accessory shaft is appropriate aligned with the chuck clamping members.