Nothing has kept him from earning victories over the Milwaukee Brewers at Wrigley Field in recent seasons, though.
Dempster looks to remain unbeaten against the defending NL Central champions at the Friendly Confines when the Cubs continue their four-game set with the Brewers on Wednesday.
The right-hander had a solid outing against Washington on April 5, allowing one run and two hits in 7 2-3 innings and left with a 1-0 lead after allowing a single.
The run charged to Dempster came when reliever Kerry Wood walked three straight batters to force in the runner for which Dempster was responsible, tying the game.
Carlos Marmol then allowed the winning run in the ninth, and the Cubs (1-4) lost 2-1.
Dempster will hope for a similar outing but a different result while looking to improve his already stellar mark against the Brewers.
He went 0-2 with a 4.24 ERA in three starts against them in 2011, but he's 15-4 with a 3.04 ERA in 25 lifetime starts versus Milwaukee, including 7-0 with a 2.42 ERA in eight at Wrigley Field.
He won seven straight before leaving without a decision in Chicago's 1-0 victory June 13 in the most recent home outing against the Brewers.
Chicago's bullpen didn't have a lead to protect in Tuesday's 7-4 loss after Pat Maholm allowed six runs in four innings. The Cubs starters had a 2.30 ERA through the first four games.
The bullpen, though, wasn't of much help in those contests, and three relievers combined to walk five in five innings Tuesday. It allowed another run and is 0-3 with a 7.24 ERA and two blown saves in 13 2-3 innings.
Manager Dale Sveum has lost the first two of this series against his former team, as the Brewers (3-2) scored five first-inning runs - highlighted by Alex Gonzalez's three-run homer.
Sveum said he's not concerned quite yet.
"We've put ourselves in situations to win ballgames, and in the major leagues, that's what you try to do every night," Sveum told the team's official website.
Yovani Gallardo will take the mound for the Brewers after allowing six runs and seven hits in 3 2-3 innings of an 11-5 loss to St. Louis in his first start Friday.
Gallardo got off to a rocky beginning last season as well, going 2-2 with a 6.10 ERA in his first seven starts, but he ended 2011 with a career-high 17 wins and a 3.52 ERA.
The right-hander has been stellar against the Cubs in recent seasons, going 3-0 with a 1.38 ERA in his last six outings against them. He's struggled, though, against Ian Stewart, who is 5 for 10 with two doubles and a pair of homers lifetime off Gallardo.
Gallardo will get solid run support if the trend from the first two games continues, as the Brewers' offense has produced seven runs in each victory. Jonathan Lucroy also homered Tuesday, and Ryan Braun, who has hit safely in the last four games, drove in his second run of the season.
''(The first inning) was pretty good. If that wind's not blowing in, it could have been really good. Braun absolutely killed that ball,'' manager Ron Roenicke said. ''But that's Wrigley Field.''
Milwaukee has won 9 of the last 11 meetings.