He's looked just fine against the Chicago Cubs in recent years.Peavy seeks his sixth consecutive win over the Cubs when the crosstown rivals continue their three-game set Tuesday night at U.S. Cellular Field.Finally healthy after making 35 total starts between 2010 and 2011, Peavy (6-2, 2.91 ERA) has been stellar in 2012, with his only two losses being 1-0 defeats. He allowed four hits and pitched all nine innings in an April 28 loss to Boston, then went seven innings against St. Louis last Wednesday despite battling an illness."I'll tell you what, I pitched better tonight than I did feeling good the last few," Peavy said after losing to the Cardinals.Peavy has dominated the Cubs in recent years, winning his last five starts against them with a 1.42 ERA. He allowed three hits in 6 1/3 innings of a 6-0 victory at Wrigley Field on May 20.The White Sox (35-32), though, had their AL Central lead trimmed to one-half game over Cleveland after dropping Monday's series opener 12-3 to the North Siders. They've lost 10 of 15 since their season-best nine-game winning streak May 23-June 1.The Cubs set season highs for runs, hits (15) and home runs (5) in the win. Bryan LaHair, Alfonso Soriano, Starlin Castro, Luis Valbuena and Geovany Soto -- playing his first game since May 16 -- all went deep."We had big hits," said Soriano, who is 9 for 26 (.346) with three homers and three doubles lifetime versus Peavy. "LaHair had a big homer, Castro had a big homer. That's the most important thing, I hope we continue doing that."Soriano is batting .333 in his last nine games at U.S. Cellular Field."We see the ball good in this ballpark. It's different. I feel comfortable in this ballpark," Soriano said.Paul Konerko and A.J. Pierzynski homered Monday for the White Sox in a losing cause."It was a night (the ball) was carrying, and (the Cubs) put it on the barrel a lot," White Sox manager Robin Ventura said.Despite Monday's loss, the White Sox have won nine of their last 13 home meetings with the major league-worst Cubs (23-44), who got some bad news Monday as top pitcher Ryan Dempster was placed on the disabled list.Dempster, whose 2.11 ERA ranks second in the majors, has thrown 22 consecutive scoreless innings and won three straight starts. However, the right-hander said Monday he's been battling tightness in his right lat muscle, and the pain finally has prevented him from taking the mound."It's just gotten harder and harder to get loose and maintain," Dempster said."I felt like I was going south in the way I was feeling versus feeling better each time."Travis Wood will oppose Peavy seeking his first win in more than a year.Wood (0-3, 4.58 ERA) is 0-2 with a 3.38 ERA in his last three outings after allowing three runs in 6 2/3 innings of a 5-3 loss to Detroit on Thursday.The left-hander, who has never faced the White Sox, is winless in his last nine starts since beating the Los Angeles Dodgers on June 15, 2011, while with Cincinnati.