Tuesday night-Wednesday morning looks like a decent candidate to not drop below 80 in Chicago. It will be partially dictated by Tuesday's high temp for an elevated starting point and would like to see a high of at least 95 on that day to raise the odds of not dropping below 80 that night.
925 mb temps are progged around 27C Tuesday night-Wednesday morning. I have noticed that it is tough to get nighttime lows much below the 925 mb temp in urban areas when there's a bit of a breeze, which we look to have. 27C is 80.6F, so it gives an idea of where the low could end up. Not a perfect system but an approximation.
If it does happen, the issue would be getting that temp to hold all through Wednesday, as it looks like a front will want to slip through late Wednesday or so.
As mentioned, Chicago's earliest 80 degree low is in late June... June 28 to be exact. So this would be almost a full 2 weeks earlier.