The White Sox, who are in third place in the American League Central Division and trail the Minnesota Twins by five games with a 25-27 record, won two out of three at Tampa Bay over the weekend.
The Dodgers, meanwhile, saw their lead shrink to two games in the National League West over San Diego after completing a seven-game home stand in which they won just two out of seven against Pittsburgh and the New York Mets.
After the series concludes on Thursday, the Dodgers fly back to California to open a three-game weekend series against the Giants in San Francisco Friday night.
How to watch the Dodgers vs. White Sox series
Where: Guaranteed Rate Field, Chicago.
Radio: AM KLAC (570), KTNA (1020) Spanish.