First Heard at a Sporting KC game: Opening night at LIVESTRONG park against Chicago, June 9th, 2011. Not sure if this dates back to Wizards days.
Based off of: Unknown.
History: The earliest known mention of the chant is 1994 in Syracuse, NY in 1994 at Bishop Ludden High School. The first person credited with origination is Jay Rodriguez in 1998 at the Naval Academy. One of the commenters below (Mid'05) noted that they recall hearing it sometime between 2001 and 2004. Another Midshipman commenter noted originating it and was class of 2003. You may see some reports of a later origination at the Naval Academy in 2003, because the team apparently didn't do to well in the interval years and no one had a reason to believe that Navy would win.
The earliest recording I can find of the Naval Academy chanting "IBTWWW" is 2009. But they did have shirts printed up in 2003 with "I Believe That We Will Win." Recordings of this showed up from college basketball teams like Utah St. and SDSU around 2009/10. It is also known to be heard at US Men's National Team games. After the popularity exploded in 2014 with the World Cup, Jeff Eisenberg from Dirty Tackle did a investigative article on the chant origins with a lot of detail. If you like this chant this is a must read article.
History since 2011: Sporting KC used #IBelieveThatWeWillWin as part of the playoff marketing campaign with full paged ads, encouraging of the hashtag on Twitter and changes to their main home page. In 2012, IBTWWW was used as part of the ad campaign for the newly branded NBC Sports Network (formerly Versus). For the 2014 World Cup it became much more popular after being used in a EPSN commercial featuring the American Outlaws.
Associated movement: Usually jumping in place (pogo-ing) once you get to the final line. Others have pumped their fist (or two) in the air with each crowd response.
Lyrics: (Call and Response)
Leader: I believe
Crowd: I believe
Leader: I believe that
Crowd: I believe that
Leader: I believe that we
Crowd: I believe that we
Leader: I believe that we will win!
Crowd: I believe that we will win!
(until crowd starts to quiet)
(Often restarted after fade out maybe 2 or 3 times max)
When you'll hear it: Maybe late in the first half if still scoreless, usually after a goal that gives us a lead, rarely after a goal that gets us equal. Possibly late in the game.
Listen to it recorded from Sporting Park:
"I Believe That We Will Win" Sporting Kansas City (downloadable) by AdAstraSKC
Sporting Kansas City 2011 Playoff Ad
Other MLS Clubs using it: New York Red Bulls (2010), Columbus Crew (2011)
2014 World Cup ESPN Promo - Celebrities
2014 World Cup ESPN Promo - American Outlaws
Find it on Twitter with Hashtag #IBTWWW
If you have more information on this chant, please comment below and will get the post updated.