The supramolecular structure of the synaptonemal complex (SC) mediates homologous chromosome synapsis and facilitates the formation of genetic crossovers during meiosis. The mammalian SC is formed of eight coiled-coil proteins which interact in specific subcomplexes and self-assemble into distinct macromolecular arrays that fulfil specific aspects of the SC’s dynamic functional architecture. Here, we report the structure of SC subcomplex SYCE2-TEX12 and its mechanism of self-assembly into fibres that define the SC’s midline longitudinal structure. X-ray crystal structures, electron microscopy, biophysical and mutational analyses reveal that SYCE2-TEX12 is assembled from 2:2 complexes in which TEX12 chains are positioned at either end of a rod-like SYCE2 dimer. These molecular building-blocks assemble laterally into 4:4 complexes, and longitudinally into fibres of potentially limitless length, which acts as string-like threads that wind around one another in intertwined fibres of up to 40-nm in width and several micrometres in length. This hierarchical assembly mechanism is reminiscent of intermediate filament proteins and results in SYCE2-TEX12 fibres that can span the entire chromosome length, thereby providing the underpinning structural support for SC elongation during meiotic chromosome synapsis.