What logical fallacies are in here?

This seems to be more of an implication than a claim. An ad Hominem (guilt by association) fallacy.  If it were syllogized further it could make a case for Fallacy of Division, or whole-to-part fallacy.

Chicago is the most corrupt city in America. (needs citation)

Obama's entire political career was spent in Chicago.

Therefore; Obama is most certainly corrupt.

I agree with the previously mentioned  ad hominem (guilt by association) and fallacy of division (and stating that "all Chicago politicians are corrupted" is also stereotyping (the fallacy) ).

I would add that the argument

'Obama spent his entire political career in Chicago, therefore he is corrupt.
 [Afterall] "You don’t get to be the head thief by being the worst thief"'

is weak analogy .

A few possibilities here. As mentioned, this argument could be said to commit the fallacy of division because it assigns to a part (one politician from Chicago) a claimed quality of the whole (politicians from Chicago, America's "most corrupt city").

This argument could also qualify as an argumentum ad hominem (abusive) if reformulated in the following manner:

• President Obama is arguing in favor of X.


• President Obama is a Chicago politician.


• Therefore, X is most certainly some form of corruption.

Perhaps we can call this "guilt by implication."