This study will evaluate the safety and effectiveness of the drug interferon-beta1a (AVONEX) in treating ulcerative colitis and examine the drug's effect on the immune system. People with ulcerative colitis have increased amounts of inflammatory chemicals (cytokines) made by immune cells in the lining of the colon. Studies have shown that interferon-beta may block the activity of these cytokines. Interferon-beta1a (AVONEX) is currently FDA-approved to treat multiple sclerosis, a disease involving inflammation of the brain and spinal cord.