This randomized, double-blind, double-dummy, parallel-group study will evaluate the efficacy and safety of ocrelizumab in comparison with interferon beta-1a (Rebif) in participants with relapsing multiple sclerosis. Participants will be randomized to receive either ocrelizumab 600 mg or matching placebo intravenous (IV) as 300 mg infusions on Days 1 and 15 for the first dose and as a single infusion of 600 mg for all subsequent infusions every 24 weeks, with placebo injections matching interferon beta-1a SC three times per week; or interferon beta-1a 44 mcg SC injections three times per week (with placebo infusions matching ocrelizumab infusions every 24 weeks). Planned duration of double-blind treatment is 96 weeks. Participants who complete the 96-week double-blind treatment will have an option to enter a single-group, active-treatment, open-label extension period, providing they fulfill the eligibility criteria.