The archaeal RNA-degrading exosome contains a catalytically active hexameric core, an RNA-binding cap formed by Rrp4 and Csl4 and the protein annotated as DnaG (bacterial type primase) with so-far-unknown functions in RNA metabolism. We found that the archaeal DnaG binds to the Csl4-exosome but not to the Rrp4-exosome of Sulfolobus solfataricus. In vitro assays revealed that DnaG is a poly(A)-binding protein enhancing the degradation of adenine-rich transcripts by the Csl4-exosome. DnaG is the second poly(A)-binding protein besides Rrp4 in the heteromeric, RNA-binding cap of the S. solfataricus exosome. This apparently reflects the need for effective and selective recruitment of adenine-rich RNAs to the exosome in the RNA metabolism of S. solfataricus.