Cut chicken into cubes, and sprinkle with thyme and pepper. Brown chicken in a Dutch oven coated with vegetable cooking spray over medium-high heat.
Whisk together flour and 1 can broth; add flour mixture, remaining 2 cans broth, and vegetables to chicken mixture. Bring to a boil; stir in rice. Cover, reduce heat, and simmer 5 minutes. Reduce heat; add cheese, stirring until melted.
Makes: 11 cups