1868 Thersites is a Jupiter Trojan asteroid that orbits in the L4 Lagrangian point of the Sun-Jupiter system, in the "Greek Camp" of Trojan asteroids. It was named after the Greek hero 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. 1869 Philoctetes was also discovered the same day by the same group.
Photometric observations of this asteroid during 1994 were used to build a light curve showing a rotation period of 10.416 ± 0.014 hours with a brightness variation of 0.14 ± 0.01 magnitude.