Cook rice according to package directions, omitting salt and fat.
While rice cooks, heat oil in a large Dutch oven over medium-high heat. Add chopped onion and next 4 ingredients, and sauté 6 minutes or until onion is tender.
Lightly spoon flour into a dry measuring cup, and level with a knife. Stir flour, tarragon, and thyme into onion mixture, and cook 1 minute, stirring frequently. Add 2 cups water, sherry, broth, and evaporated milk; bring mixture to a boil, stirring occasionally. Reduce heat, and simmer 20 minutes or until slightly thick, stirring occasionally. Stir in cooked rice and chicken; cook 10 minutes or until thoroughly heated.