Melt the butter in a pot over medium-high heat. Whisk in the flour until a smooth paste forms, about 1 minute.
Gradually whisk in the chicken broth, milk, and light cream. Cook and stir until the mixture thickens and comes to a boil (5 to 10 minutes). Reduce the heat to medium; stir in the cooked chicken.
Return the soup to a boil and cook until the chicken is heated through (5 to 10 minutes).
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