I did my undergrad and master's at McGill and will move to the US for PhD next year. I find it very difficult to believe you will turn down UIUC in favour of McGill for Chem Eng.
This isn't just a US vs Canada thing, because McGill engineering is nowhere near as good as even UofT or Waterloo engineering. Sure, Montreal is an absolutely fantastic city, but your career prospects will be far better if you have a doctoral degree from UIUC.
As for the visa entry issue, that's up to you to figure out your priorities, I doubt anyone here will really be able to help you with that.