Quoting Georgetown University Professor Anthony Clark Arend:
Dr. King made these remarks in a speech to 26,000 African-American high school and college students on April 18, 1959. The students had come to Washington, D.C. to demonstrate their support for the 1954 Supreme Court decision in Brown v. The Board of Education, outlawing racial segregation in public schools. (The speech can be found in I Have  Dream: Writings and Speeches that Changed the World (James Melvin Washington, ed., 1992, p. 34).

For an excellent resource site on Martin Luther King's life and work, go to  http://www.civilrights.org/resources/mlk/