Graphene, or single-layered graphite, with its high crystallinity and interesting semimetal electronic properties, has emerged as an exciting two-dimensional material showing great promise for the fabrication of nanoscale devices. Thin, elongated strips of graphene that possess straight edges, termed graphene ribbons, gradually transform from semiconductors to semimetals as their width increases, and represent a particularly versatile variety of graphene. Several lithographic, chemical and synthetic procedures are known to produce microscopic samples of graphene nanoribbons, and one chemical vapour deposition process has successfully produced macroscopic quantities of nanoribbons at 950 degrees C. Here we describe a simple solution-based oxidative process for producing a nearly 100% yield of nanoribbon structures by lengthwise cutting and unravelling of multiwalled carbon nanotube (MWCNT) side walls. Although oxidative shortening of MWCNTs has previously been achieved, lengthwise cutting is hitherto unreported. Ribbon structures with high water solubility are obtained. Subsequent chemical reduction of the nanoribbons from MWCNTs results in restoration of electrical conductivity. These early results affording nanoribbons could eventually lead to applications in fields of electronics and composite materials where bulk quantities of nanoribbons are required.