A Study of LY2623091 in Participants With High Blood Pressure

Inclusion Criteria: * Have a history of hypertension. * If participants are naïve to treatment of hypertension, or have not been treated with any antihypertensive medications within the 30 days immediately prior to screening: * Have seated systolic (SBP) of ≥140 and \<170 millimeters of mercury (mmHg) at screening and at the end of the lead-in period. * If participants are currently being treated for hypertension: * Are taking a stable dose of 1 or 2 antihypertensive medications for at least the previous 30 days. A combination antihypertensive medication from 2 classes is considered as 2 antihypertensive medications. * Are willing to discontinue the antihypertensive medications during the study. * Have seated SBP of ≥140 and \<170 mmHg at the end of the lead-in period. * Have a body mass index (BMI) ≥18.5 and \<40 kilograms/m\^2. Exclusion Criteria: * Have a history of severe hypertension (defined as SBP ≥180 mmHg and/or diastolic (DBP) ≥120 mmHg), secondary hypertension, symptomatic postural hypotension, or hospitalization due to hypertension. * Have SBP ≥180 mmHg and/or DBP ≥110 mmHg at screening, lead-in period, or randomization. * Have a history of hospitalization due to hyperkalemia, or history of drug discontinuation due to elevated serum potassium levels. * Have a serum potassium ≤3.5 or \>5.0 millimoles per liter (mmol/L). * Have an estimated glomerular filtration rate (eGFR) \<50 milliliters/minute/1.73 m\^2.