What is Martin Luther King, Jr.'s claim in his "I Have a Dream" speech?

Martin Luther King's “I Have a Dream” speech is essentially a persuasive speech, delivered in 1963 during the March on Washington.

People giving persuasive essays and speeches intend to convince their audiences to agree with their position on a certain issue. This “position” is often referred to as a claim. To be effective, a claim has to be well-expressed and credible. Achieving this credibility depends on several things, including the speaker's reputation and how well his or her claim is supported.

At about 16 minutes, King's speech was fairly long. To find his claim in that much text, you have to find the sentence expressing King's central message. What does he say that, if you stripped away all the rest of the text, still makes his main point?

I think the sentence that does the best job of this is the first sentence of the third paragraph:

But one hundred years later, the Negro still is not free.

Everything else is in the speech is used to support this claim. King goes on to use many different rhetorical and oratorical devices; he gives many different examples and cites many different facts, but all of it is intended to show how African-Americans still suffered the effects of racial prejudice in 1963.