A method for operating a chain stitch sewing machine and a chain stitch sewing machine, the chain stitch sewing machine having a pair of sewing members comprising a needle which pierces a sewing material and a gripper disposed below a sewing material rest, which can be moved along a movement path, where an upper thread is guided with the needle through the sewing material resting on the sewing material rest, which is linked to a lower thread. The lower thread is fed to a retaining element and is held in said element that is moved with regard to its direction of movement and/or speed of movement to the sewing material rest according to a movement path of a pivoting movement of the gripper in particular along a circular-arc-segment-shaped movement path.