It's rather difficult to understand what you're asking, because BY definition, endemic to Chicago means it is native to Chicago, and means it is NOT native to the rest of the USA. Do you have an example animal here that is not endemic to Chicago, but is native to Chicago but not all of the USA? "Native to only X but not all of Y," if Y is not a subset of X, and if X is a subset of Y, is endemism, nothing else.
You're misquoting me. I said "Native to X but not all of Y", not "Native to *only* X but not all of Y", there is a big difference.
A bird which is native to Chicago and Rockford and nowhere else is not endemic to Chicago, or endemic to Rockford, or native to the whole of N. America.