The answer is Mexico.
Although other countries have a huge history of migrational movements, like India and China (which are the main protagonists of the phenomenon called 'brains migration', which means the migratory flux of highly qualified professionals from their country of origin), their targets are well distributed among other first world countries, like Canada, Australia, and central-western European nations.
However, Mexico, although not a relevant exporter of a highly qualified working force, due to proximity and the country's poor socioeconomic status, is the most contributor to the North-American foreign-born population. For decades, there have been huge illegal migrational movements of people that go to work in low-specialization jobs, like masons and maids.