Inclusion Criteria:  18 years of age or older Documented paroxysmal, persistent, or permanent non-valvular atrial fibrillation (AF) At increased risk of stroke or systemic embolism defined as CHADS2 score (Risk of Stroke with AF". VA Palo Alto Medical Center and at Stanford University: the Sportsmedicine Program and the Cardiomyopathy Clinic: Congestive/Hypertension/Age/Diabetes/Stroke): ≥ 2 or a CHA2DS2-VASc score (Congestive/Hypertension/Age/Diabetes/Stroke/Vascular disease/Sex) ≥ 3 Deemed, by investigator, to be unsuitable or contraindicated for long term oral anticoagulation therapy due to high bleeding risk To have suitable anatomy for percutaneous Left Atrial Appendage occlusion procedure with a single Omega™ device Able and willing to comply with the required medication regimen post-device implant Able to understand and willing to provide written informed consent to participate in the study Able to and willing to return for required follow-up visits and examinations.  Exclusion Criteria:  Requires long-term oral anticoagulation therapy for any indication other than atrial fibrillation Contraindicated for or allergic to aspirin/clopidogrel, warfarin or novel oral anticoagulant (NOAC) use Implanted with a mechanical heart valve prosthesis thus requiring long term oral anticoagulation Has any contraindications for a percutaneous catheterization procedure (e.g. subject is too small to accommodate the transoesophageal echocardiogram (TEE/TOE) probe or required catheters, or subject has active infection or bleeding disorder) Women of childbearing potential who are, or plan to become, pregnant during the time of the study (method of assessment per physician discretion) Stroke or transient ischemic attack (TIA) within 6 weeks prior to implant procedure Underwent any cardiac or non-cardiac intervention or surgery within 30 days prior to implant, or intervention or surgery is planned within 60 days after implant procedure Myocardial infarction (MI) within 90 days prior to implant New York Heart Association Class IV Congestive Heart Failure Left ventricular ejection Fraction (LVEF) ≤ 30% Reversible cause of AF (i.e. secondary thyroid disorders, acute alcohol intoxication, trauma, recent major surgical procedures) Left atrial appendage is obliterated or surgically ligated Resting heart rate >110 bpm Thrombocytopenia (defined as < 70,000 platelets/mm3) or anaemia with haemoglobin concentration of < 10 g/dl (i.e. anaemia as determined by the investigator which would require transfusion) Actively enrolled or plans to enrol in a concurrent clinical study in which the active treatment arm may confound the results of this trial Active endocarditis or other infection producing bacteraemia Subject has a known malignancy or other illness where life expectancy is less than 2 years Impaired renal function with eGFR (Estimated Glomerular Filtration Rate) <40 ml/min/1.73 m2 More than mild hepatic failure, i.e. ALT (Alanine Aminotransferase), AST (Aspartate Aminotransferase), or Alkalic Phosphatase >2× upper limit of normal  Echocardiographic Exclusion Criteria:  Intracardiac thrombus - including Left Atrial Appendage - visualized by echocardiographic imaging Existing circumferential pericardial effusion >2mm Significant mitral valve stenosis (i.e. mitral valve area <1.5 cm2) High risk patent foramen ovale (PFO), defined as an atrial septal aneurysm (atrial septal excursion >15mm; excursion defined as maximal protrusion of the ASA (Atrial Septal Aneurysm) beyond the plane of the atrial septum during cardiac cycle) or large shunt (substantial passage of bubbles, i.e. ≥ 25, within 3 cardiac cycles from appearing in the right atrium) Complex atheroma with mobile plaque of the descending aorta and/or aortic arch Cardiac tumour Left Atrial Appendage anatomy cannot accommodate an Omega™ device (as per IFU) Placement of the device would interfere with any intracardiac or intravascular structure.