Rodlike fibrous structures are increasingly found with biomacromolecules, e.g. silks, elastin, and collagen. Here we propose a multiblock copolymer model that can lead to these larger-scale structures. One component consists of highly regular blocks, whereas the blocks of another, incompatible component exhibit a wide range of lengths. Rods readily form when these lengths have a bimodal distribution and a well-defined periodicity along the chain. Orientation in a flowing liquid assists association of rods, as is likely in the spinning of silks, which have comparable repetitive sequences. The model suggests that rodlike structures should be available in similarly designed synthetic polymers. This route would be distinct from existing routes that employ rigid monomers, e.g. aramids.