Klimesh was discovered on 18 June 2000, by NASA's and JPL's Near-Earth Asteroid Tracking program (NEAT) with the Maui Space Surveillance System (MSSS) at the Haleakala Observatory site on the island of Maui, Hawaii, in the United States. The body's observation arc begins 15 years prior to its official discovery observation, with a precovery from the Digitized Sky Survey taken at the Australian Siding Spring Observatory in September 1985.