The purpose of this study is to determine whether the addition of surgical ablation to planned mitral valve surgery for patients with persistent or longstanding persistent AF (within 6 months prior to randomization) reduces the incidence of postoperative heart arrhythmia compared to mitral valve repair with medication therapy alone. This is a randomized, multi-center trial which will enroll 260 subjects who will be randomized in a 1:1 fashion to: (a) mitral valve surgery plus surgical ablation or (b) mitral valve surgery without ablation (control group). All patients will undergo ligation or excision of the left atrial appendage. Patients assigned to the ablation group will be further randomized (1:1) to one of two lesion sets: (1) pulmonary vein isolation only or (2) biatrial Maze lesions. The target population for this trial consists of adult patients with mitral valve disease requiring surgical intervention and persistent or longstanding persistent atrial fibrillation. All patients who meet the eligibility criteria may be included in the study regardless of gender, race or ethnicity. The primary efficacy endpoint is freedom from AF, which will be measured by 3-day continuous monitoring at 6 months and 12 months post-ablation. The primary safety endpoint is a composite of death, stroke, serious cardiac events (heart failure, myocardial infarction), cardiac re-hospitalizations, transient ischemic attack, pulmonary embolism, peripheral embolism, excessive bleeding, deep sternal wound infection/mediastinitis, damage to specialized conduction system requiring permanent pacemaker, damage to peripheral structures, such as the esophagus, within 30 days post-procedure or hospital discharge (whichever is later).