Looking at
the precinct maps you can see that whites in Chicago voted for Clinton (since it is unfortunately a rather segregated city). Lakeview is over 80% white and gave over 80% of the vote to Clinton. Lincoln Park is also over 80% white and "only" gave about 77% of the vote to Clinton. North Center, which is "only" 77% white, gave over 80% of the vote to Clinton. The only community area in Chicago that Trump won was Mount Greenwood (probably due to having a high population of police officers).
Actually, as I'm typing up this post it occurs to me that your math is off. Let's assume that the demographics of voters in Cook County match those of the population (likely false but let's see what happens if that were true). Let's also try to specifically estimate the non-Hispanic white vote in Cook County, which accounts for roughly 44% of the population according to the 2010 Census. Clinton won Cook County 74-21. If we allocate the other 56% of the voters 80% to Clinton and 20% to Trump+others, we get 45% of the total vote for Clinton from there. The other 29% of the vote needs to come from the 44% of non-Hispanic whites, which brings us to Clinton getting 66% of the non-Hispanic white vote in Chicago, under these assumptions. If Clinton had only won 36% of the white vote (even just the non-Hispanic white vote), you wouldn't even be able to get her to 74% by allocating every single remaining vote to her. I'm not sure where your error is.