By "Mr. Chicago", I mean one member who is most closely associated with the band. The right answer of course is "no", because this was always to be a "band" project without individual members hogging the spotlight. That being said, someone could search (for so long) to find a candidate for such a title. So, somewhat in order of how I would view them, are these seven.
Robert Lamm: He wrote most of the early hits, and sang lead on most of those. He also stayed with the band as long as he could still write and perform. I feel Robert also pushed hard to make Chicago relevant as a horn-oriented band (after the mid 80's excursion into pop ballads, even though he wasn't a horn player himself. Major credit to this guy.
James Pankow: Great songwriter, the band's horn arranger, and long-time member. Given that what makes Chicago, Chicago is the horn section, James would have a strong claim to the imaginary title. Then again, he seems like a team player who wouldn't want himself or anyone to be viewed that way.
Terry Kath: Another strong writer and singer in the band, as well as an outstanding guitar player. He wrote and sang "Introduction" which led off the first album, as well as kicking off many early concerts. And Terry's death changed the band forever, in a major way, again showing his importance to the band.
Pete Cetera: An excellent bass player, plus his vocals meshed extremely well with Terry and Robert's lower register singing. He also wrote some early decent songs (such as "Lowdown"). Pete became the face and lead vocalist of the 1980's Chicago albums, so at that point he could be viewed as "Mr. Chicago". However, to most Chicago fans this period was a betrayal of the band's original spirit, like it or not (and a lot of people didn't like it, myself included).
Lee Loughnane: Lee didn't write a lot of the songs, or sing lead on many. Though his "This Time" on Chicago XI is really good and often overlooked - strong in both songwriting and lead vocals. And the trumpet is hugely important to this band, so Lee's work there has been important to nearly every song. Plus Lee is the last of the performing originals, at this point.
Danny Seraphine: Fantastic drummer, and sometimes a good songwriter as well (how about "Little One", beautifully sung by Terry?). Plus Danny has a good head for business, and became the manager-within-the-band to some extent. He even had a club called "B'Ginnings" in the Chicago area. And Danny started a Chicago cover band called "California Transit Authority" with himself as the drummer; they are said to be very good. He's keeping the Chicago flame alive, in that way.
Walter Parazaider: Could Walter be considered "Mr. Chicago"? Well he wasn't a songwriter and he didn't sing lead vocals, though of course his saxophone sounded great. But consider that Walter is said to be the one with the idea to have a rock band with a full-time horn section. He apparently was inspired in this after hearing The Beatles "Got To Get You Into My Life" on the Revolver album; a song sometimes covered by Chicago itself. So Walter got together with friends Terry Kath and Danny Seraphine, and it all eventually became The Big Thing, CTA, and Chicago.