Yes they have. However the White Sox do have a slightly better head to head record than the Cubs. The Sox have beat the Cubs 37 times and the Cubs have beat the Sox 35 times (since the inception of interleague play), as of the beginning of the 2010 season.
However, when it counted the most way back in 1906 when the two teams played each other in the City's only Cross-Town World Series to date; The Mighty White Sox beat the heavily favored Cubs 4 games to 2 to win the White Sox AND the City of Chicago its very FIRST World Series Championship.
The Cubs have not won a World Series title since 1908. That's 102 years ago! This is the longest such drought for a franchise in all of sports. The Cubs haven't appeared in a World Series since 1945.
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