A cellulose synthesis complex (CSC) with a 'rosette' shape is responsible for synthesis of cellulose chains and their assembly into microfibrils within the cell walls of land plants and their charophyte algal progenitors. The number of cellulose synthase proteins in this large multisubunit transmembrane protein complex and the number of cellulose chains in a microfibril have been debated for many years. This work reports a low resolution structure of the catalytic domain of CESA1 from Arabidopsis thaliana (AtCESA1CatD) determined by small-angle scattering techniques and provides first experimental evidence for the self-assembly of CESA into a stable trimer in solution. The catalytic domain was over-expressed in Escherichia coli and using a two-step procedure, it was possible to isolate monomeric and trimeric forms of AtCESA1CatD. The conformation of monomeric and trimeric AtCESA1CatD proteins were studied using small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS). A series of AtCESA1CatD trimer computational models were compared with the SAXS trimer profile to explore the possible arrangement of the monomers in the trimers. Several candidate trimers were identified with monomers oriented such that the newly synthesized cellulose chains project towards the cell membrane. In these models, the class specific region (CSR) is found at the periphery of the complex and the plant-conserved region (P-CR) forms the base of the trimer. This study strongly supports the 'hexamer of trimers' model for the rosette CSC that synthesizes an 18-chain cellulose microfibril as its fundamental product.