The clamping device (10) for grasping a thread during the production of a woven seam is arranged at the end of a draw-through gripper and comprises a first and a second clamping element, whereby the first and the second clamping element (20, 24) for grasping the thread can be tightened against one another by means of a pneumatic cylinder. The first clamping element comprises two interspaced cylinder surfaces (20) and the second clamping element has a cylinder surface (24). The arrangement of the cylinder surfaces (20, 24) is such that the axes of the cylinder surfaces are parallel to one another and are essentially located at a right angle to the axis of the pneumatic cylinder, and such that, when the pneumatic cylinder is in an extended position, the cylinder surface (24) of the second clamping element is located between both cylinder surfaces (20) of the first clamping element.