Outcome Measures: Quantitative neuroimaging measures of central nervous system (CNS: i.e. brain and spinal cord) tissue destruction and clinical and functional (i.e. electrophysiological) measures of neurological disability will be collected every 6-12 months. Additionally, biomarkers focusing on analysis of cerebral spinal fluid (CSF) B cells and immunological responses to EBV will be collected at baseline and during treatment. The trial is currently powered using progression of brain atrophy as detected by SIENA methodology as the primary outcome measure. However, this may not be the most sensitive outcome available. In recognition of this, the trial has an adaptive design: it incorporates analysis of the progression of CNS tissue destruction, as measured by quantitative MRI markers, and clinical/paraclinical markers, defined as secondary outcome measures, in the first 30 enrolled patients during the year long pre-treatment baseline prior to randomization. All defined outcome measures collected in the first 30 enrolled patients will be transformed into z-scores and compared for the robustness of longitudinal change over the coefficient of variation. As a result, the primary outcome measure of this trial will be the comparison of individualized rates of brain atrophy progression between the rituximab and placebo groups after 2 years of treatment; unless the predetermined analysis establishes that one of the secondary outcome measures has a higher z-score than the brain atrophy measurement. In this case, the primary outcome would be the efficacy of rituximab versus placebo in inhibiting patient-specific slopes of functional or structural deterioration as measured by this more sensitive biomarker of CNS tissue destruction.