The Immigration Act of 1965.
President Johnson signing the 1965 Immigration Act
The 1965 Immigration Act brought about a radical change in the way that new migrants to the US were to be processed. Prior to the 1965 Act there were strict limits on the numbers of new migrants who could enter from different parts of the world. In short, migration was controlled along the lines of race and ethnicity. The 1965 Act changed this. It set a quota on the number of Visa’s that were available to new entrants to the US but changed the emphasis so that 170,000 could be issued to people from the Eastern Hemisphere and 120,000 to people from the Western Hemisphere, with no more than 20,000 available to migrants from any given country. These new rules worked on a ‘first come, first served’ basis, removing the possibility of migrants being turned away because of race, religion or ethnicity.
Senator Ted Kennedy, speaking as the Bill was debated, claimed that the change was needed for several reasons, and sought to play down the fears of some Americans that the new bill may affect workers in the US. He said, “This [old] system violates the basic principle of American democracy, the principle that values and rewards each man on the basis of his merit as a man. It has been un-American in the highest sense, because it has been untrue to the faith that brought thousands to these shores even before we were a country.”
Wikipedia – looks at the causes and impact of the 1965 Act.
America.gov – detailed history of immigration policy in the United States.