X-ray scattering and various optical techniques are utilized to study the aggregation process and chromonic liquid crystal phase of the anionic monoazo dye Sunset Yellow FCF. The x-ray results demonstrate that aggregation involves pi-pi stacking of the molecules into columns, with the columns undergoing a phase transition to an orientationally ordered chromonic liquid crystal phase at high dye concentration. Optical absorption measurements on dilute solutions reveal that the aggregation takes place at all concentrations, with the average aggregation number increasing with concentration. A simple theory based on the law of mass action and an isodesmic aggregation process is in excellent agreement with the experimental data and yields a value for the "bond" energy between molecules in an aggregate. Measurements of the birefringence and order parameter are also performed as a function of temperature in the chromonic liquid crystal phase. The agreement between these results and a more complicated theory of aggregation is quite reasonable. Overall, these results both confirm that the aggregation process for some dyes is isodesmic and provide a second example of a well-characterized chromonic system.