Chronic Obstructive Pulmonary disease (COPD) patients with chronic hypercapnic respiratory failure are more likely to develop exacerbations. Non-invasive ventilation has been proposed to treat acute respiratory failure but little information is available about the benefits of home non-invasive ventilation in COPD patients with chronic hypercapnic respiratory failure surviving an acute hypercapnic respiratory failure. The purpose of this study is to determine whether home non-invasive ventilation can reduce recurrent acute hypercapnic respiratory failure in COPD patients who survived an episode of acute hypoxemic respiratory failure (AHRF) treated by Non-invasive ventilation (NIV).