So the Kentucky Supreme Court held last week in Hill v. Petrotech Resources Corp., following a modern trend (though one from which some state courts have dissented). The premise is that the ban on “prior restraints” means that speech may not be restricted prior to a decision on the merits that it falls within an unprotected category, such as libel. So a preliminary injunction based on a mere likelihood that the speech will be found libelous — and preliminary injunctions generally rest on such likelihood-of-success-on-the-merits decisions — violates the First Amendment, but a permanent injunction against certain statements based on a finding on the merits that those particular statements are libelous would be constitutional.
I’ve argued here that this is generally correct as a matter of First Amendment law, both as a matter of First Amendment logic and given the Court’s decisions in Kingsley Books, Inc. v. Brown or Pittsburgh Press Co. v. Pittsburgh Commission on Human Relations. But some state courts have read their state constitutions as barring even permanent injunctions in libel cases, and there is considerable 19th century authority supporting that view.
The Kentucky Supreme Court held that both the First Amendment and the Kentucky Constitution allows permanent injunctions. Query whether that’s correct given the text and original meaning of the Kentucky provision (“Every person may freely and fully speak, write and print on any subject, being responsible for the abuse of that liberty.”), though if you want to opine on that you might want to read the court’s explanation of how it is interpreting the Kentucky provision.