This quote comes from Justice Harlan's eloquent majority opinion in the famous case of Cohen v. California, 403 US 15 (1971), which you may remember as the case involving the California man who wore a jacket reading "F*ck the Draft."
Cohen is a relatively short decision in an even shorter series of cases dealing with the elusive "fighting words" doctrine. While the First Amendment may protect most of our speech, there are certain forms of speech it does not protect, in this case, "abusive epitaphs which, when addressed to the ordinary citizen, are, as a matter of common knowledge, inherently likely to provoke violent reaction." Cohen.
Cohen, however, sets the bar for the determination of fighting words very high. Despite Cohen's rather provocative attire, the Court found it entirely outside of California's right to restrict his wearing it. The Court lists numerous rationals for why Cohen's conduct did not rise to the level of unprotected speech, including the observation that the public could easily avert their eyes from the patch, that Cohen wore the jacket to a courthouse (this seems counter-intuitive as a reasoning at first blush, but consider that the Court is particularly concerned not with what a person does in public, but with what a captive audience is forced to endure in the quiet of their own home and it makes more sense), and, finally, that to enact a ban on one of our beloved four letter words would affect much, much more than the intended speech. Specifically, such a ban could well work its way into affecting artistic choice.
Since Cohen, the Supreme Court has never upheld a "fighting words" statute. Before Cohen only they only upheld such a conviction in Chaplinsky (Chaplinsky v. State of New Hampshire, 315 US 568 (1942)). Although Chaplinksy was never officially overruled by Cohen, the assumption is that the Court realized the error of its former ways and Chaplinsky is no longer good law, as far as its holding.