Does Free Speech Include Speech You Disagree With?

Should speech that offends have a place in America? According to the First Amendment of the Constitution the answer is yes.
*** UPDATE 4.18.2017 ***

A victory for free speech. The court ruled to compel this institution of higher learning to do what they are required to do – and that is to expose their students to ideas that may be different from their own, ideas that challenge them, rather than just simply follow the status quo: