This article has been retracted as it is essentially identical in title and technical content with the published article “Idempotent Elements of the Endomorphism Semiring of a Finite Chain,” by Ivan Trendafilov and Dimitrinka Vladeva, published in Comptes Rendus de L'Académie Bulgare des Sciences 66 (2013), no. 5, 621–628 (see [1]).