The eukaryotic exosome is a macromolecular complex essential for RNA processing and decay. It has recently been shown that the RNase activity of the yeast exosome core can be mapped to a single subunit, Rrp44, which processively degrades single-stranded RNAs as well as RNAs containing secondary structures. Here we present the 2.3 A resolution crystal structure of S. cerevisiae Rrp44 in complex with single-stranded RNA. Although Rrp44 has a linear domain organization similar to bacterial RNase II, in three dimensions the domains have a different arrangement. The three domains of the classical nucleic-acid-binding OB fold are positioned on the catalytic domain such that the RNA-binding path observed in RNase II is occluded. Instead, RNA is threaded to the catalytic site via an alternative route suggesting a mechanism for RNA-duplex unwinding. The structure provides a molecular rationale for the observed biochemical properties of the RNase R family of nucleases.