1868 Thersites is a Jupiter trojan asteroid that orbits in the L4 Lagrangian point of the Sun–Jupiter system, in the "Greek camp" of Jupiter trojan. It was named after the Greek soldier Thersites, who fought during the Trojan War. It was discovered by Cornelis Johannes van Houten, Ingrid van Houten-Groeneveld and Tom Gehrels on September 24, 1960 in Palomar, California at the Palomar Observatory.