There's apparently something of a belief that big cities can't be hit by tornadoes, or at least protected from them. Perhaps because it's almost never happened—only the Salt Lake City tornado of 1999 and one in Atlanta in 2008 come to mind in my lifetime. Or perhaps it has to do with theories proposed by Ted Fujita:

In the past 40 years, the city of St. Louis and the surrounding suburbs of St. Louis County have been hit 22 times, although none of them were in the tiny skyscraper heart of the city. There are three possible reasons for that. First, the central city may produce a "heat island" in which turbulent rising air disrupts the formation of small tornadoes(keep in mind that most tornadoes are small). The second possibility is that the "roughness" created by the skyscrapers causes turbulence that disrupts the formation of small tornadoes. The third, is, of course, the idea that tornadoas are rare, and the central city is very small. So it is a matter of coincidence.

Professor Fujita of the University of Chicago suggested that the "heat island" effect takes hold for small tornadoes when a city reaches a population of about 1,000,000. There seems to be a lack of small tornadoes in the central cities of Chicago, Tokyo, and London. These are the only three cities that have been carefully studied over a long time.

Tornadoes obviously hit the Chicago area with some frequency. But there hasn't been one to hit downtown since May of 1876, an F3 that killed 2 and injured 35—surprisingly fortunate numbers given that it tore up Wabash Avenue ("an ill-fated thoroughfare").  A tornado did hit Chicago in 1961, as Tom Skilling points out: an F2, moving from 91st and Western to 68th and Lake Michigan, causing seven million dollars in damage, injuring 115 people, and killing one. Flickr user Edward Schonsett has some remarkable amateur photographs of the aftermath. There's some thought that the city's proximity to Lake Michigan may reduce the chance of tornadoes, but I haven't read anything that suggests a tornado anywhere in the city isn't possible.

While reading up on Chicago tornadoes, I did come across something interesting in regards to the city's effect on weather, the LaPorte Weather Anomaly: "a dramatic increase in unpleasant weather conditions starting around 1925, roughly corresponding with the growth in productivity of the Chicago-Gary iron and steel industry."