We report rheological, X-ray, and dielectric investigations on a chromonic liquid-crystalline system formed by aqueous solutions of a food coloring agent, Sunset Yellow, in the absence and upon addition of salt. The salt-concentration dependence of the steady-state viscosity at low shear rates has a non-monotonic variation and is qualitatively similar to the behavior seen in wormlike micellar systems, a surprising result since chromonic systems are expected to be non-micellar in character. More interestingly, for a particular low concentration of the salt (20 mM), the viscosity increases by 3 orders of magnitude in comparison with that of the pure chromonic material. The dynamic (oscillatory) rheological data bring out features which can be described in terms of a microstructure formation. X-ray and dielectric studies show that certain characters of the aggregates formed by the Sunset Yellow molecules are not altered by the addition of salt.