(I'm a bit late with this actually - he's up to 1003 now)
On June 12th, Paul Konerko started for the White Sox, and the White Sox beat the Cardinals 6-1. That game marked the 1000th time the White Sox won a game with Konerko in the starting lineup. Since 1920, only 3 other White Sox players have started in 1000 wins - Frank Thomas (1,020), Luke Appling (1,078) and Nellie Fox (1,143).
The only other active players with 1000 wins for their team are Derek Jeter and Chipper Jones. Since 1920, 66 players other than Konerko have won 1000 games they started for a single franchise, and 44 of them are in the Hall of Fame. 4 more are still on the ballot, 5 haven't become eligible yet, and 1 is banned for life.