Tyler Saladino hit a game-ending RBI single, and the White Sox put a damper on the Cubs' trade for Chapman with a 5-4 victory.
J.B. Shuck sparked the winning rally with a leadoff single against Mike Montgomery (3-5), who was acquired in a deal with Seattle last Wednesday. Shuck advanced on Dioner Navarro's sacrifice and Saladino followed with a bouncer into center field.
Dan Jennings (4-2) got two outs for the win.
The Cubs trailed 4-2 before Dexter Fowler and Anthony Rizzo each hit an RBI single in the ninth. They had runners on first and second with two out when Jennings struck out Jason Heyward to escape the threat.
Javier Baez hit a two-run homer for the Cubs, who were coming off a nice weekend series in Milwaukee.
Todd Frazier hit a three-run drive off Jake Arrieta and Miguel Gonzalez pitched 6 2/3 innings of two-run ball, helping the White Sox improve to 5-5 in interleague play. Melky Cabrera made an outstanding leaping catch in the first, robbing Kris Bryant of a home run.
Kyle Hendricks (9-6, 2.27 ERA) looks to continue his breakout year on Tuesday night against White Sox RHP James Shields (4-12, 4.99 ERA).