Boil chicken breasts for 15-20 minutes. Remove from heat and dice into small pieces.
In a large saucepan, prepare rice according to package directions, substituting chicken broth for water.
Preheat oven to 350°. Grease a 9 x 13 in baking dish.
In a large skillet, saute onion, carrots, green pepper, and mushrooms in olive oil until soft, about 5 minutes. Add wine and continue cooking for 2-3 minutes.
Pour wine and vegetable mixture over rice and mix well. Stir in chicken.
In a medium saucepan, combine cream cheese, evaporated milk, and cheddar cheese. Cook over medium heat until cheese is melted and mixture is smooth. Add to rice mixture and stir well.
Pour mixture into prepared baking dish.
Sprinkle sliced almonds over the top of the casserole. Cover dish with aluminum foil and bake at 350° for 35 minutes. Remove foil and continue baking for 10-15 minutes or until bubbly.