The study will enroll up to 165 patients, randomized in a 1:1:1 ratio to 1 of 3 treatment groups (55 patients in each group): KBP-5074 0.25 mg once daily (QD), KBP-5074 0.5 mg QD, or placebo QD. Randomization will be stratified to balance enrollment for key variables that may influence safety and/or efficacy evaluations, including estimated Glomerular Filtration Rate (eGFR) (30 versus 29 mL/min/1.73 m2) and Systolic Blood Pressure (SBP) (160 versus \<160 mmHg). The study will be approximately 5 months in duration with 84 days of double-blind treatment. The study will consist of an up to 4-week screening period; 2-week, open-label (placebo) run-in period; 84-day double-blind treatment period; and a 4-week post-treatment safety follow-up period. Patients will be sampled for plasma pharmacokinetics (PK). Total KBP-5074 levels will be assessed in patients treated with active drug. A total of 4 PK samples will be collected from each patient, including Day 1 (prior to discharge), Day 14 pre-dose, Day 28 pre-dose, and End of Study Visit (Day 98)/Early Termination Visit. The pre-dose samples assume that patients will be dosed in the unit on those days above. If patients are not dosed in the unit on those days, a flexible PK sample will be collected during each of these visits.Safety will be assessed systematically, and an independent data monitoring committee will perform cumulative reviews of safety data at regular intervals during the study. Serum potassium levels, serum creatinine, and blood pressure will be closely monitored throughout the study. At Screening, patients must have uncontrolled hypertension, defined as resting trough cuff seated SBP 140 mmHg, based on the mean of the last 2 consecutive blood pressure readings at Screening in the clinic. In all cases, dose and frequency of concurrent antihypertensive medications are expected to be maintained without change for 30 days prior to randomization in order to ensure that blood pressure is stable. In general, patients should not add nor adjust dose and/or types of the antihypertensive medications they are receiving during the screening period and throughout the duration of the study (unless they develop hypertensive crisis or symptomatic hypotension). Patients will be advised to maintain their normal diet and avoid alcohol or potassium-rich foods/drinks during the study period. No potassium supplements are permitted, unless clinically indicated to treat hypokalemia until serum potassium values are within the normal range. Potassium-sparing agents are not permitted. After completion of the screening period and the qualifying Screening Visit, patients who meet all eligibility criteria (except those criteria scheduled to be assessed after the Screening Visit), will enter the 2-week, open-label (placebo) run-in period. At the end of the run-in period, patients will be re-assessed for eligibility, including compliance to study drug received during the run-in period, which must be \>80% and 120% (i.e. placebo and stable antihypertensive medication, i.e. no change in antihypertensive medication). If a patient is found to be ineligible during Screening, a 1-time re-screening is allowed if the Investigator believes that the patient's condition has changed and the patient may be eligible before the re-screening tests. Please note that a new patient number should be assigned to any re-screened patient, and all the procedures defined in the protocol for the Screening Visit and during the run-in period must be repeated. Patients who meet all eligibility criteria at the end of the screening period and run-in period will be randomized (stratified based on eGFR 30 versus 29 mL/min/1.73 m2 and SBP 160 versus \<160 mmHg) into the study on Day 1. All randomized patients will receive double-blind treatment for 84 days. Patients will be followed for 4 weeks for safety assessments after the last dose of study drug. A subset of patients who still meet eligibility criteria at the end of the run-in period (Visit 3) will undergo 24-hour ambulatory blood pressure monitoring (ABPM) on Day 1, Day 40, and Day 82.