• Improvement in Clinical Activity Score by 2 or more points [ Time Frame: 2,4,6 and 12 months after the first infusion ] [ Designated as safety issue: No ]
  

• Decrease in disease severity by ≥2 NOSPECS classes [ Time Frame: 2,4,6 and 12 months after first infusion ] [ Designated as safety issue: No ]
  
• Decrease in proptosis by ≥2 mm [ Time Frame: 2,4,6 and 12 months after first infusion ] [ Designated as safety issue: No ]
  
• Decrease in lid aperture width by ≥3 mm [ Time Frame: 2,4,6 and 12 months after first infusion ] [ Designated as safety issue: No ]
  
• Improvement in extraocular motility by ≥8 degrees [ Time Frame: 2,4,6 and 12 months after first infusion ] [ Designated as safety issue: No ]
  
• Improvement in a GO-specific quality of life score of ≥ 6 points [ Time Frame: 2,4,6 and 12 months after first infusion ] [ Designated as safety issue: No ]
  
• Failure rate, defined as need for additional therapy (excluding cosmetic surgery) for the eye disease [ Time Frame: 52 weeks ] [ Designated as safety issue: No ]
  
• Composite of decrease of CAS ≥ 2 points and no need for additional therapy for the eye disease versus either CAS decrease of < 2 points or need for additional therapy [ Time Frame: 52 weeks ] [ Designated as safety issue: No ]
  

Detailed Description: Before any treatment is given, careful eye and thyroid physical examinations will be performed and the patients will have several thyroid blood tests, a test to count the white cells in the blood, and a CT scan of the head and eyes. A thyroid ultrasound will be performed at the end of the first visit. A close-up photograph of the face will be taken and patients will be given a short questionnaire about how their eyes are feeling and how the eye disease is affecting their quality of life. Each study subject will receive either 2 infusions of rituximab (each 1000 mg; given 2 weeks apart) or 2 intravenous infusions of saline. Patients will return to Rochester 2 weeks after the first intravenous infusion in order to receive the second infusion. They will then return to Rochester four more times; 2 months apart for the first 3 return visits (weeks 8, 16 and 24 following the first infusion) and 6 months later (approximately 52 weeks following the first infusion) for the final visit to have the same blood tests performed. The CT scan will be repeated at 52 weeks. The thyroid ultrasound will be repeated at the 24 weeks and 52 weeks visits. Patients will be assigned to one of these two groups in a random manner (like flipping a coin) and neither they nor the physicians will know until the study is completed whether they received saline or the study drug.