Participants are randomly assigned to one of two treatment groups: one group takes atorvastatin; the other takes a placebo (a look-alike pill that has no active ingredient to fight sarcoidosis). Both groups take the pills by mouth once a day for 12 months. When treatment begins, participants begin to have their prednisone dosage tapered (reduced). The tapering is done over 8 weeks until the dose is reduced by 90 percent. Patients are evaluated periodically to determine if the two groups differ in how long they can remain on the reduced dose of prednisone without having their symptoms recur, requiring an increase in the prednisone dose. A full battery of tests is done at the initial screening visit and at the 26- and 52-week follow-up visits, requiring hospitalization for 3-5 days. Additional interim outpatient assessments are done at 6, 12, 18 and 36 weeks.