As I'm sure you've heard, it's been awhile for the White Sox. Before 2004, the Red Sox hadn't won a World Series since 1918? The White Sox had them beat by a year.
The Chicago White Sox won the World Series in 1917. In 1919, eight White Sox players conspired to lose the World Series, and they did. In 1920, the White Sox were in the thick of the pennant race down to the final few days of the season, but fell short after revelations about the '19 Series tore the club apart. And it would be nearly four decades before the White Sox won another American League pennant.
Owner Charles Comiskey's health wasn't good in the 1920s, but he didn't give up after the Black Sox scandal. In 1922, the White Sox paid San Francisco $100,000 for third baseman Willie Kamm, which at the time (and for a while afterward) was a record sum for one player. Five years later, the Sox sent $75,000 and four players to the Portland club for shortstop Bill Cissell. But though Comiskey was obviously capable of the grand gesture, the details often seemed to escape him, and the result was a long string of second-division finishes in the American League standings.