 This study will determine the safety and feasibility of using a β-blocker in this case carvedilol in the treatment of pediatric patients with Left Heart Failure LHF in children with Pulmonary Arterial Hypertension PAH. Carvedilol affects the nervous system, the same system that is highly activated in response to stress in patients with PAH. Each patient is administered a dosage of carvedilol, according to their weight. This dosage is increased incrementally over the span of the study, if the patient responds well to the drug. The study will determine whether the potential adverse side effects of carvedilol outweigh the possible positive results in reducing LHF. The hypothesis of this study predicts that carvedilol will have positive effects in treating LHF, similar to their use in treatment of Right Heart Failure RHF. This is a single-centered pilot study. Each patient will be studied for approximately 31 weeks. 