The purpose of the research is to determine whether treating atrial fibrillation with surgical ablation during scheduled mitral valve surgery is better than mitral valve surgery by itself without the surgical ablation. Surgical ablation of atrial fibrillation is a technique used by surgeons to deaden atrial heart tissue and block electrical signals that may be causing your heart to beat irregularly. There are no new procedures being tested in this study; both mitral valve surgery and surgical ablation are used regularly in patients who have mitral valve problems and atrial fibrillation, although no surgical ablation devices have been approved by the Food and Drug Administration for the treatment of atrial fibrillation. What is not known with certainty, is whether patients with atrial fibrillation who are having planned mitral valve surgery would do better if they also had surgical ablation rather than medication alone to treat their atrial fibrillation.