We are known locally and everywhere else for our political corruption. I think it extends way past politics though. I have lots of local connections – the "I'll scratch your back you scratch mine" mentality is strong around here. I would be shocked if we were unique for it, but it seems to be a common feature of the land.
edit - from an outsiders perspective, I thought somewhere like Washington or Vegas would be considered more way more corrupt than Chicago. I guess it is different types of corrupt, as Chicago managed the version where everybody left and they ran out of money. Perhaps the problem is they weren't corrupt enough.
Maybe you are thinking of Detroit... Chicago's doing pretty well economically and culturally.
Washington, D.C. and Las Vegas are not known for the same style of grafty, political-machine corruption as, say, Chicago or NYC Tammany Hall. The former two don't internally operate at the same scale as a Chicago and I doubt most of the rest of the US cares about their internal goings-on.