The purpose of this study is to test the hypothesis that renal denervation is safe and reduces systolic blood pressure (SBP) in patients with uncontrolled hypertension on one, two, or three standard antihypertensive medications compared to a sham control in the same population. In this study, "uncontrolled hypertension" is defined as an office systolic blood pressure (SBP) ≥ 150 mmHg and \<180 mmHg, an office Diastolic Blood Pressure (DBP) ≥90 mmHg and a 24-hour Ambulatory Blood Pressure Monitoring (ABPM) average SBP ≥140 mmHg to \<170 mmHg, all of which are measured at Screening Visits. Data obtained will be used to confirm the effect of renal denervation on elevated blood pressure in patients on 1, 2 or 3 antihypertensive medications.