In Old Chief v. United States, the Supreme Court stated that evidence offered by the Government in a criminal case has “fair and legitimate weight” if it tends to show that a guilty verdict would be morally reasonable. This Article focuses on that proposition. First, it discusses the ways in which Old Chief’s analysis rests upon a broadened understanding of evidentiary relevance. Second, it argues that significant theoretical difficulties impede any effort to determine whether evidence tends to show that a guilty verdict would be morally reasonable. Third, it argues that adopting Old Chief’s conception of relevance would necessitate significant changes in the rules relating to jury nullification. Specifically, if a prosecutor were permitted to present evidence in part for the purpose of demonstrating that a guilty verdict would be morally reasonable, the defendant might be entitled to present evidence in part for the purpose of demonstrating that a guilty verdict would be morally unreasonable; the defendant would have a Fifth and Sixth Amendment right to argue, during his or her closing argument, that the Government’s evidence fails to show that it would be morally reasonable to convict; and the defendant would be entitled to a jury instruction that informs the jurors, at a minimum, that the Government’s evidence has been admitted in part for the purpose of persuading them that a guilty verdict would be morally reasonable.