Inclusion Criteria:  Diagnosis of CVID according to the international consensus document (ICON)  a Age 4 years or above  b. Serum IgG at least 2 standard deviations below the age adjusted normal  c. Decreased serum IgA and/or serum IgM  d. Abnormal specific antibody response to immunization  e. Exclusion of secondary immunodeficiency  On replacement immunoglobulin for at least 6 months and willing to maintain throughout study Granulomatous-lymphocytic interstitial lung disease with a lymphocytic component diagnosed by lung biopsy prior to study entry, wedge biopsy preferred. Persistence or worsening of interstitial lung disease measured on serial CT imaging of the lung at least 6 months apart, with the latest assessment within 2 months of study entry. Signed written informed consent Willing to allow storage of biological specimens for future use in medical research. Females of childbearing potential must use a highly effective form of birth control such as hormone-based contraceptive, intrauterine device, or double barrier method.  Exclusion Criteria:  History of hypersensitivity to abatacept or any of its components Has received any lymphocyte depleting agents including anti-CD20 monoclonal antibodies, alemtuzumab, ATG in the preceding 6 months Has received abatacept, cyclophosphamide, tumor necrosis factor inhibitors, or pulse steroids (defined as >15mg/kg/day of methylprednisone or corticosteroid equivalent) within the past 3 months History of HIV infection (positive PCR) Chronic untreated hepatitis B or C (positive PCR) Active tuberculosis (TB) by positive QuantiFERON gold. If history of latent TB, then must supply evidence of completing treatment. Persistent Epstein-Barr Virus (EBV) load ≥ 1,000 units/mL blood checked twice at least 1 month apart Other uncontrolled infections Live vaccine given within 6 weeks of the start of the trial Malignancy or treated for malignancy within the past year Currently pregnant or breast feeding Life expectancy less than 1 month Subjects unwilling to self-administer or have a parent/caregiver self-administer subcutaneous injections at home Other conditions that the investigators feel contraindicate participation in the study