As defects frequently govern the properties of crystalline solids, the precise microscopic knowledge of defect atomic structure is of fundamental importance. We report a new class of point defects in single-layer transition metal dichalcogenides that can be created through 60 degrees rotations of metal-chalcogen bonds in the trigonal prismatic lattice, with the simplest among them being a three-fold symmetric trefoil-like defect. The defects, which are inherently related to the crystal symmetry of transition metal dichalcogenides, can expand through sequential bond rotations, as evident from in situ scanning transmission electron microscopy experiments, and eventually form larger linear defects consisting of aligned 8-5-5-8 membered rings. First-principles calculations provide insights into the evolution of rotational defects and show that they give rise to p-type doping and local magnetic moments, but weakly affect mechanical characteristics of transition metal dichalcogenides. Thus, controllable introduction of rotational defects can be used to engineer the properties of these materials.