The best way to thicken Chicken Tortilla Soup is with a slurry. A slurry is equal parts cold water and cornstarch, whisked together and added to a soup or sauce to thicken it. Keep in mind that the soup or sauce must be hot, and simmering, in order for the slurry to work, and the water added to the cornstarch must be cold. Typically 2 tablespoons of cornstarch added to 2 tablespoons of cold water is enough to thicken a soup or sauce. Add it slowly whisking into the soup until the desired thickness is achieved.