According to Keith Law (Insider article), not until 2015.
(Not sure how to block quote this in this window, so I'll use quotes and rely on the link as my 'source'.)
It helps that the NL Central is one of the weaker divisions, but the Cubs' rebuilding has barely broken ground at this point -- the new front office has barely had a chance to clear the land. Their moves this winter, other than the trade of reliever Andrew Cashner for first base prospect Anthony Rizzo and pitcher Zack Cates, were largely about moving money around and keeping the 2012 product respectable without making dangerous long-term commitments such as the one wandering aimlessly around left field these days. (And it should be quite respectable, maybe even a little better if their gambles on starting pitchers whose peripheral stats were better than their ERAs work out.)
Chicago's farm system is thin up top but has a lot of high-risk, high-upside players in its lowest levels; even their extended spring training club will be fun to watch this year. But the Cubs' best chance to engineer a turnaround will probably come from trades, starting with Matt Garza but perhaps extending to players such as Geovany Soto or Carlos Marmol if they can re-establish their value with solid 2012 performances; they bought low on Ian Stewart and Chris Volstad and could end up selling high if either player fulfills his former first-round promise in the next two years.
By the 2013-14 offseason, they'll have a significant amount of cash to spend but only a handful of less expensive players in significant roles, so cashing in Garza for the maximum return looks like the critical step in their rebuilding process.
They will most likely contend next in ... 2015"
Not really much new in here, but hey... it's spring.
I'm not sure exactly what his definition of 'contention' is. He mentions a 'playoff spot' in the intro. So I'm not real sure why 2014 would be out of the question, particularly given the two WCs.
I would sure hope 85 or so wins (my rough barometer of 'contention') isn't out of the question for the next three full seasons.