The primary objective of this study is to determine the efficacy of peginterferon beta-1a in reducing the annualized relapse rate (ARR) in participants with relapsing multiple sclerosis (RMS) at 1 year. The secondary objectives of this study are to determine whether peginterferon beta-1a, at 1 year when compared with placebo, is effective in reducing the total number of new or newly enlarging T2 hyperintense lesions on brain magnetic resonance imaging (MRI) scans, reducing the proportion of participants who relapse, and slowing the progression of disability.