The purpose of this study is to compare the safety and effectiveness of an experimental device called the Laminar Left Atrial Appendage Closure System with a commercially available left atrial appendage closure device that is used to close off the left atrial appendage to eliminate a potential source of blood clots. The study focuses on people who have atrial fibrillation, a condition in which the heart beats with an irregular rhythm. This irregular rhythm increases the chance of blood pooling and clotting inside the heart; the blood clots can break loose from the heart and cause a stroke. Previous research has shown that closing the heart outpouching (left atrial appendage) eliminates the area where blood clots can form, ultimately lowering the chance of a stroke occurring. Closing the left atrial appendage using the Laminar investigational device or a commercially approved device is the main procedure of the study. Participants will be randomly assigned to 1 of 2 groups. Group 1 will receive the Laminar Left Atrial Appendage Closure Device, and Group 2 will receive a commercially available left atrial appendage closure device.