Shortening eukaryotic poly(A) tails represses mRNA translation and induces mRNA turnover. The major cytoplasmic deadenylase, the Ccr4-Not complex, is a conserved multisubunit assembly. Ccr4-Not is organized around Not1, a large scaffold protein that recruits two 3'-5' exoribonucleases, Caf1 and Ccr4. We report structural studies showing that the N-terminal arm of yeast Not1 has a HEAT-repeat structure with domains related to the MIF4G fold. A MIF4G domain positioned centrally within the Not1 protein recognizes Caf1, which in turn binds the LRR domain of Ccr4 and tethers the Ccr4 nuclease domain. The interactions that form the nuclease core of the Ccr4-Not complex are evolutionarily conserved. Their specific disruption affects cell growth and mRNA deadenylation and decay in vivo in yeast. Thus, the N-terminal arm of Not1 forms an extended platform reminiscent of scaffolding proteins like eIF4G and CBP80, and places the two nucleases in a pivotal position within the Ccr4-Not complex.