In its prion form, Ure2p, a regulator of nitrogen catabolism in Saccharomyces cerevisiae, polymerizes into filaments whereby its C-terminal regulatory domain is inactivated but retains its native fold. The filament has an amyloid fibril backbone formed by the Asn-rich, N-terminal, "prion" domain. The prion domain is also capable of forming fibrils when alone or when fused to other proteins. We have developed a model for the fibril that we call a parallel superpleated beta-structure. In this model, the prion domain is divided into nine seven-residue segments, each with a four-residue strand and a three-residue turn, that zig-zag in a planar serpentine arrangement. Serpentines are stacked axially, in register, generating an array of parallel beta-sheets, with a small and potentially variable left-hand twist. The interior of the filament is mostly stabilized not by packing of apolar side chains but by H-bond networks generated by the stacking of Asn side chains: charged residues are excluded. The model is consistent with current biophysical, biochemical, and structural data (notably, mass-per-unit-length measurements by scanning transmission electron microscopy that gave one subunit rise per 0.47 nm) and is readily adaptable to other amyloids, for instance the core of Sup35p filaments and glutamine expansions in huntingtin.