The assembly of static supramolecular structures is a culminating event of developmental programs. One such structure, the proteinaceous shell (called the coat) that surrounds spores of the bacterium Bacillus subtilis, is composed of about 70 different proteins and represents one of the most durable biological structures known. The coat is built atop a basement layer that contains an ATPase (SpoIVA) that forms a platform required for coat assembly. Here, we show that SpoIVA belongs to the translation factors class of P-loop GTPases and has evolutionarily lost the ability to bind GTP; instead, it uses ATP hydrolysis to drive its self-assembly into static filaments. We demonstrate that ATP hydrolysis is required by every subunit for incorporation into the growing polymer by inducing a conformational change that drives polymerization of a nucleotide-free filament. SpoIVA therefore differs from other self-organizing polymers (dynamic cytoskeletal structures and static intermediate filaments) in that it uses ATP hydrolysis to self-assemble, not disassemble, into a static polymer. We further show that polymerization requires a critical concentration that we propose is only achieved once SpoIVA is recruited to the surface of the developing spore, thereby ensuring that SpoIVA polymerization only occurs at the correct subcellular location during spore morphogenesis.