Inclusion Criteria  Patients willing and capable of giving written informed consent, which includes compliance with the requirements and restrictions listed in the consent form A diagnosis of Graves' disease based on the presence of hyperthyroidism associated with detectable anti-thyrotropic hormone (TSH) receptor autoantibodies (TRAb). Patients must be euthyroid under control on stable medical regimen and every effort will be made to maintain the euthyroid status for the entire duration of the clinical trial A moderate-to-severe GO, defined as the presence of at least one of the following criteria: an exophthalmos ≥2 mm compared with normal values for sex and race; presence of inconstant to constant diplopia; a lid retraction ≥2 mm, lasting since no longer than 9 months Active GO: CAS (4) ≥ 3 out of 5 points in the most affected eye Male and female patients of age: 18-75 years AST, ALT and CPK levels ≤ 3 times the upper value of normal range Women of childbearing potential (WOCBP, namely not in menopause or in menopause since less than two years; in all other instances women will be considered as non-WOCBP) and men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year (as indicated in Appendix) for at least 6 and 7,5 months, respectively, after the last dose of the investigational drug (see also 2014_09_HMA_CTFG_Contraception.pdf, namely the "2014 CTFG Reccommendtions related to contraception and pregnancy testing in clinical trials"). Compliant patient, regular follow-up possible  Exclusion Criteria  Optic neuropathy Corticosteroids or immunosuppressive treatment for GO in the last 3 months. Use of selenium in the last 3 months or during the clinical trial Previous surgical or radiant (orbital irradiation) treatment for GO Radioiodine treatment for hyperthyroidism over the last 3 months, as it can affect GO (4) Statin treatment in the last 3 months Contraindications to GC: hypersensitivity to the active substance or to any of the excipients; uncontrolled hypertension, uncontrolled diabetes; history of peptic ulcer; urinary infections, glaucoma, systemic fungal infections, systemic infections unless appropriate therapy is employed, idiopathic thrombocytopenic purpura, cerebral edema associated with malaria. Use of medications interfering with GC or increasing the risk of GC-related adverse events (see prohibited therapies) Pregnant or lactating females as determined by positive serum or urine HCG test at baseline Acute or chronic liver disease All factors that could increase the risk of rhabdomyolysis, in particular medications that could increase this risk (see prohibited therapies) Contraindications to statins, namely: hypersensitivity to atorvastatin or other statins, or hypersensitivity or intolerance to the medication excipients such as lactose; current or past liver diseases; alterations of liver tests. Medications interfering/interacting with statins (see prohibited therapies) Relevant Malignancy Recent (≤1 year) history of alcoholism or drug abuse Mental illness that prevent patients from comprehensive, written informed consent