In the European context we trace it back to the Ludi Romani (Roman Games) held at the Circus Maximus (lit. big circuit) in Rome. The agitatores (Chariot drivers) competed together as teams during races, the first of these teams were apparently created during the Kingdom period sometime between the 8th c. and the 6th c. BC. according to the Roman historian Tertullian. He lived many centuries after this period in the 2nd and 3rd centuries AD and so the accuracy of his accounts of the history of the sport may suffer from chronological distance from the events he writes about, but he is our prime source. Tertullian tells us that the first teams to be established were the 'Whites' representing Winter and the 'Reds' representing Summer.

During the Republican era new teams including the Greens and the Blues were created, during Justinian's reign in the 6th c AD the Nika riots, the prologue to our modern Soccer and Hockey riots occurred and the tradition of team Chariot racing continued within the Byzantine Empire after the fall of Rome in the West.

There's a lot to the topic of the chariot teams, it ties in with notions of Citizenship and what it meant to be Roman, to religious identity and how the act of participating in the games as a spectator or as a a sportsman was an integral part of that, to Roman notions of social mobility and opportunity and who could and could not access those.

It's great place to start for anyone interested in learning more about the history of Sport or the history of Rome or both, as it's simultaneously very familiar in certain respects such as team rivalries and high earning stars and very different in other respects such as the overt religious overtones.

Sources

http://ancienthistory.about.com/od/colosseum/a/CircusMaximus.htm

http://www.vroma.org/~bmcmanus/circus.html

http://en.wikipedia.org/wiki/Chariot_racing

http://penelope.uchicago.edu/~grout/encyclopaedia_romana/circusmaximus/circusmaximus.html

http://www.reddit.com/r/AskHistorians/comments/1vtoj2/who_were_the_blues_and_the_greens_in_the/