Inclusion Criteria:  Signed and dated Ethics Committee (EC) approved study consent form prior to study related procedures ≥ 18 years old  Chronic symptomatic Heart Failure (HF) documented by the following:  NYHA class III or ambulatory NYHA class IV within last 12 months AND ≥ 1 HF hospital admission (with HF as the primary, or secondary diagnosis); or treatment with intravenous (IV) or intensification of oral diuresis for HF in a healthcare facility (emergency department/acute care facility) within the 12 months prior to study entry; OR an NT-pro BNP value > 150 pg./ml in normal sinus rhythm, > 450 pg./ml in atrial fibrillation, or a BNP value > 50 pg./ml in normal sinus rhythm, > 150 pg./ml in atrial fibrillation within the past 6 months. In the judgment of the investigator, subject is on stable Guideline Directed Medical Therapy (GDMT) for heart failure and management of potential comorbidities according to current ACCF/AHA/ESC Guidelines and that is expected to be maintained without change for 3 months Elevated LA (or PCWP) pressure of > 15 mmHg at rest or > 25 mmHg during supine ergometer exercise stress test, as measured at end-expiration; AND the LA (or PCWP) exceeds right atrial pressure (RAP) by > 5 mmHg at rest or > 10 mmHg during supine ergometer exercise stress test as measured at end-expiration Willing to attend study follow-up assessments for up to 5 years  Exclusion Criteria:  Severe heart failure defined as one or more of the below:  ACC/AHA/ESC Stage D heart failure, non-ambulatory NYHA Class IV HF If BMI < 30, Cardiac index < 2.0 L/min/m2 If BMI ≥ 30, cardiac index < 1.8 L/min/m2 Inotropic infusion (continuous or intermittent) within the past 6 months Patient is on the cardiac transplant waiting list LVEF < 20%  Presence of significant valve disease defined by the site cardiologist as:  Mitral valve regurgitation defined as grade > 3+ MR or > moderate MS Tricuspid valve regurgitation defined as grade > 2+ TR Aortic valve disease defined as > 2+ AR or > moderate AS MI and/or any therapeutic invasive cardiac procedure within past 3 months; or current indication for coronary revascularization Valve replacement or surgical annuloplasty within the past 12 months Stroke or transient ischemic attack (TIA) within the past 6 months Hemodynamic instability within 30 days of scheduled implant procedure Patient requiring surgery under general anesthesia for any reason within 30 days of scheduled implant procedure Clinically diagnosed hypertrophic obstructive cardiomyopathy, constrictive pericarditis or other infiltrative cardiomyopathy (eg, hemochromatosis, sarcoidosis) at the time of screening per central screening committee Has renal insufficiency as determined by creatinine (S-Cr) level > 2.5 mg/dL or estimated-GFR < 25ml/min/1.73 m2 by CKD-Epi equation; or currently requiring dialysis Significant hepatic impairment defined as 3× upper limit of normal of transaminases, total bilirubin, or alkaline phosphatase  Right ventricular dysfunction, defined by the site cardiologist as:  More than mild RV dysfunction as estimated by TTE; OR TAPSE <1.4 cm; OR RV size ≥ LV size as estimated by TTE; OR Echocardiographic or clinical evidence of congestive hepatopathy; Evidence of pulmonary hypertension with PVR >4 Wood units Performance of the 6 minute walk test with a distance <50m OR >600m Subject is contraindicated to receive either dual antiplatelet therapy or warfarin (analogue); or has a documented coagulopathy Known hypersensitivity to anticoagulation therapy or contrast agent, which cannot be adequately medicated Known hypersensitivity to Nickel and/or Tantalum In the judgment of the investigator, life expectancy <12 months for noncardiovascular reasons In the opinion of the investigator and Central Screening Committee, the subject is not an appropriate candidate for the study Anatomy or implantable device that is not compatible with or could potentially interfere with the Edwards Transcatheter Atrial Shunt System as determined by the Investigator and Central Screening Committee Active endocarditis or infection within 3 months of scheduled implant procedure Currently participating (e.g., undergoing trial specific exams/treatment/procedures) in an investigational drug or device study. Note: trials requiring extended follow-up for products that were investigational but have since become commercially available are not considered investigational trials. Patient is a current intravenous drug user Positive serum pregnancy test in female subjects of child-bearing potential or nursing mothers or planning on becoming pregnant during the duration of the trial Patient is under guardianship Known pre-existing shunting, determined to be clinically significant by the investigator and Central Screening Committee Patients with a CRT lead in the coronary sinus