I KNOW this is going to get you going.
Recently, a group called the National Foundation for American Policy conducted a study called "Coming to America: Immigrants, Baseball and the Contributions of Foreign-Born Players to America's Pastime" (link opens .pdf file).
It's a good overview of the history of foreign-born players in baseball, noting in particular the huge increase in foreign-born players in recent years. In the 2006 season, for example, fully 23.3% of all players were born outside the USA and nearly half of those (46%) are from the Dominican Republic alone.
The study includes a list of all foreign-born players by country and by team, up-to-date through August 31, 2006. The Cubs have ten players listed -- nine Hispanic players and Ryan Dempster, who is from Canada.
Well worth your time and thought.