Single-molecular-layer MoS2, prepared by exfoliation of lithium-intercalated MoS2 in water or alcohols, was deposited on supports such as carbon black and alumina. X-ray diffraction patterns show that the stacking of MoS2 layers can be perfectly turbostratic. The restacked MoS2 may or may not have water-bilayers between them, depending on the deposition conditions. A special form of the Debye fomula for a turbostratically stacked layer system is introduced and calculated diffraction patterns are compared with the experimental results. On heating, the turbostratic stacking converts to an ordered stacking, accompanied by a structural transformation of the MoS2 layers from a distorted octahedral coordination to a trigonal-prismatic coordination along with dramatic changes in the optical and electrical properties.