Abstract: A holder for a tangential chasing tool is supported in a tiltable manner in a thread cutter head which opens automatically. The holder has a chaser seat as well as a clamping plate including a guide claw. The clamping plate secures the dovetail portion of the chaser tool with the aid of a clamping jaw and two clamping screws. Exchangeable intermediate disks having different wedging angles, are insertable into the chaser seat. The bottom edge of said guide claw of the clamping plate has a convex shape, whereby the chaser tool is securely held in the holder without the need for a plurality of chaser holder sets and without any substantial modification of the holder structure.