Bring rice, 4 cups chicken broth, and 1 seasoning packet from rice mix to a boil in a saucepan over medium-high heat. Cover; reduce heat to low, and simmer 20 miutes or until liquid is absorbed and rice is tender.
Meanwhile, melt 3 Tbsp. butter in a large skillet over medium heat; add mushrooms, onion, and celery, and cook, stirring often, 10 to 12 minutes or until tender.
Melt 1/4 cup butter in a Dutch oven over medium heat; whisk in flour, and cook, whisking constantly, 1 minute, or until thickened and bubbly. Gradually whisk in remaining 6 cups broth, and cook, stirring often, 8 to 10 minutes or until slightly thickened. Whisk in half-and-half and wine. Stir in mushroom mixture, chicken, and rice. Cook, stirring occasionally, 5 to 10 minutes or until thoroughly heated. (Do not boil.)