Spectacular advances in structural and molecular biology have added support to the 'RNA world' hypothesis, and provide a mandate for chemistry to explain how RNA might have been generated prebiotically on the early earth. Difficulties in achieving a prebiotically plausible synthesis of RNA, however, have led many to ponder the question posed in the title of this paper. Herein, we review recent experimental work on the assembly of potential RNA precursors, focusing on methods for stereoselective C-C bond construction by aldolisation and related processes. This chemistry is presented in the context of a broader picture of the potential constitutional self-assembly of RNA. Finally, the relative accessibility of RNA and alternative nucleic acids is considered.