We use the macromolecular moments method of Chakraborty et al. [Phys Fluids, 34, 093109 (2022)] to calculate the complex viscosity of an aqueous suspension of polyhyaluronic acid. We do so by first calculating the equilibrium structure of the macromolecule, which leads us to its principal moments of inertia. Inserting these moments into the main results of general rigid bead-rod theory, yields from first principles, the complex viscosity of an aqueous suspension of polyhyaluronic acid. For polyhyaluronic, we find that one bead of a shish-kebab corresponds to one monomer of polyhyaluronic. Comparing our results with published complex viscosity measurements on polyhyaluronic acid suspensions, uncovers good agreement, and even better agreement with hydrodynamic interaction.