The justices did not comment Monday in refusing to review a Colorado Supreme Court ruling in favor of the university.
Churchill faced condemnation and calls for his dismissal over an essay describing some victims of the Sept. 11, 2001, terrorist attacks as "little Eichmanns," a reference to Adolf Eichmann, the Nazi leader who helped orchestrate the Holocaust.
The university investigated whether the piece was protected under the First Amendment and found that it was.
But while the investigation was under way, other academics accused Churchill of plagiarism and fraud in scholarly writings, which led to his termination in 2007. None of the allegations concerned the Sept. 11 essay.