The self-assembly of proteins into higher order structures is both central to normal biology and a dominant force in disease. Certain glutamine/asparagine (Q/N)-rich proteins in the budding yeast Saccharomyces cerevisiae assemble into self-replicating amyloid-like protein polymers, or prions, that act as genetic elements in an entirely protein-based system of inheritance. The nuclear pore complex (NPC) contains multiple Q/N-rich proteins whose self-assembly has also been proposed to underlie structural and functional properties of the NPC. Here we show that an essential sequence feature of these proteins--repeating GLFG motifs--strongly promotes their self-assembly into amyloids with characteristics of prions. Furthermore, we demonstrate that Nup100 can form bona fide prions, thus establishing a previously undiscovered ability of yeast GLFG nucleoporins to adopt this conformational state in vivo.