Chicago had a five-game winning streak snapped and saw its lead over Detroit in the American League Central reduced to two games. Both clubs have 14 contests left in the season.
Chen (11-12) gave up five hits over 6 2/3 innings and struck out four. Kelvin Herrera then worked 1 1/3 innings and Greg Holland survived a two-out double in the ninth for his 14th save.
The White Sox loaded the bases in the fourth with no one out only to have Chen escape the jam.
Chris Sale (17-7) suffered the loss after surrendering the three runs on eight hits with eight strikeouts over 6 2/3.