The original band membership consisted of saxophonist Walter Parazaider, guitarist Terry Kath, drummer Danny Seraphine, trombonist James Pankow, trumpet player Lee Loughnane, and keyboardist/singer Robert Lamm. Parazaider, Kath, Seraphine, Pankow and Loughnane met in 1967 while students at DePaul University. Lamm was recruited from Roosevelt University. The group of six called themselves "The Big Thing", and played top 40 hits. Realizing the need for both a tenor to complement baritones Lamm and Kath, and a bass player because Lamm's use of organ bass pedals did not provide "adequate bass sound", they added local tenor and bassist Peter Cetera.  While gaining some success as a cover band, the group began working on original songs. In June 1968, at manager James William Guercio's request, The Big Thing moved to Los Angeles, California, and signed with Columbia Records. The band changed its name to "Chicago Transit Authority". It was while performing on a regular basis at the Whisky a Go Go nightclub in West Hollywood that the band got exposure to more famous musical artists of the time. Subsequently, they were the opening act for Janis Joplin and Jimi Hendrix. As related to group biographer, William James Ruhlmann, by Walt Parazaider, Jimi Hendrix once told Parazaider, "'Jeez, your horn players are like one set of lungs and your guitar player is better than me.'"  Their first record (April 1969), the eponymous Chicago Transit Authority, is a double album, which is rare for a band's first release. The album made it to No. 17 on the Billboard 200 album chart, sold over one million copies by 1970, and was awarded a platinum disc. The album included a number of pop-rock songs - "Does Anybody Really Know What Time It Is?", "Beginnings", "Questions 67 and 68", and "I'm a Man" - which were later released as singles. For this inaugural recording effort the group was nominated for a Grammy Award for 1969 Best New Artist of the Year.  According to Peter Cetera, the band was booked to perform at Woodstock in 1969, but promoter Bill Graham, with whom they had a contract, exercised his right to reschedule them to play at the Fillmore West on a date of his choosing, and he scheduled them for the Woodstock dates. Santana, which Graham also managed, took Chicago's place at Woodstock, and that performance is considered to be Santana's "breakthrough" gig. A year later, in 1970, when he needed to replace headliner Joe Cocker, and then Cocker's intended replacement, Jimi Hendrix, Graham booked Chicago to perform at Tanglewood which is considered by some to be a "pinnacle" performance.  After the release of their first album, the band's name was shortened to Chicago to avoid legal action being threatened by the actual mass-transit company of the same name.

Answer this question "What happened next" by extracting the answer from the text above.
According to Peter Cetera, the band was booked to perform at Woodstock in 1969,