Patients without a documented history of AF but who present with a CHA2DS2- VASc of => 2 and HASBLED of => 2 and will undergo a valve or CABG (structural heart) procedure with direct visual access to the LAA will be eligible to participate based upon the inclusion and exclusion criteria defined in this protocol. Up to 2000 patients will enroll at up to 40 sites and will be randomized 2:1 (2 with AtriClip to 1 without AtriClip. Subjects who not develop Post-operative Atrial Fibrillation (POAF) will be followed for 30 days for safety. Subjects who develop POAF and receive the AtriClip will be followed for 365 days post index procedure.