The purpose of this study is to test the safety and efficacy of escalating doses of panobinostat in sickle cell disease. Panobinostat (Farydak) is made by Secura Bio Pharmaceuticals and is not approved by the Food and Drug Administration (FDA) for sickle cell disease. Panobinostat is only available for treatment of sickle cell disease in clinical trials like this one. Studies have shown that increasing the amount of fetal hemoglobin (HbF) in the blood may prevent sickling of the red blood cells and reduce complications of sickle cell disease. Studies in the lab and in patients with other conditions, such as cancer, have shown that panobinostat increases HbF levels and has an anti-inflammatory effect in human blood.