Treatment of Resistant Hypertension by Prevention of T-Cell Co-Stimulation

Inclusion Criteria: * Men and women 18 to 65 years of age with hypertension, treated with three or more anti-hypertensive drugs, one being a diuretic, and * having a systolic blood pressure \>150 mmHg in the clinic and daytime average \>150 mmHg on ambulatory blood pressure monitoring Exclusion Criteria: * Medical history of secondary cause of hypertension, severe obesity (BMI \>35), severe psychiatric disorders, cancer in the last 5 years other than nonmelanoma skin cell cancers, herpes zoster or cytomegalovirus that resolved less than 2 months before * Inability to return for abatacept treatment and follow-up for 24 weeks. * Inability to understand or complete study-related assessments. * Current abuse of drugs or alcohol. * Receipt of any live vaccines within 3 months of the anticipated first dose of study medication. * Evidence of active or latent bacterial or viral infections at the time of potential enrollment, including human immunodeficiency virus (HIV) * Risk for tuberculosis * Abnormal laboratory values including positive hepatitis B surface antigen, hemoglobin \< 8.5 g/dL, white blood cell count \< 3000/mm3, platelets \< 100,000/mm3, creatinine \> 2.5 times the upper limit of normal (ULN), alanine aminotransferase or aspartate aminotransferase \> 2 times the ULN.