This paper proposes to discuss the origin of Chou Tun-yi`s周敦 (1017-73) T`ai-chi t`u 太極圖 Diagram of the Supreme Ultimate, a Chinese diagram of the creation and evolution of the universe. It serves as the theoretical basis for all later cosmological speculations in the Sung Ming Neo-Confucianism. I discussed the traditional hypotheses regarding the origin of the Diagram of the Supreme Ultimate in detail. Most scholars believe that Chou`s Explanation of the Diagram grew out of a long Taoist and Buddhist tradition. Authorities accept the claim that Chou received the Diagram of the Supreme Ultimate itself from the Taoist Ch`en T`uan. Yet whether Chou received the diagram from Ch`en T`uan is debatable. Although his interpretations on transmission of the diagram are quite elaborate, they can not guarantee whether or not Mu Hsiu actually gave the diagram to Chou Tun-yi. Previous studies have regarded that the Diagram of the Supreme Ultimate that Antedates Heaven contained in the Tao Tsang as the prototype for the Diagram of the Supreme Ultimate, yet my investigation of these materials verifies that it was not created before the Sung dynasty.