The synaptonemal complex (SC) keeps homologous chromosomes in close alignment during meiotic recombination. A hallmark of the SC is the presence of its constituent protein SYCP3 on the chromosome axis. During SC assembly, SYCP3 is deposited on both axes of the homologue pair, forming axial elements that fuse into the lateral element (LE) in the tripartite structure of the mature SC. We have used cryo-electron tomography and atomic force microscopy to study the mechanism of assembly and DNA binding of the SYCP3 fibre. We find that the three-dimensional architecture of the fibre is built on a highly irregular arrangement of SYCP3 molecules displaying very limited local geometry. Interaction between SYCP3 molecules is driven by the intrinsically disordered tails of the protein, with no contact between the helical cores, resulting in a flexible fibre assembly. We demonstrate that the SYCP3 fibre can engage in extensive interactions with DNA, indicative of an efficient mechanism for incorporation of DNA within the fibre. Our findings suggest that SYCP3 deposition on the chromosome axis might take place by polymerization into a fibre that is fastened to the chromosome surface via DNA binding.