Combine the chicken pieces and vinaigrette in a large ziptop bag. Seal and massage the bag and place it on a tray. Refrigerate and allow the chicken to marinade 30 minutes to several hours.
Preheat the oven to 375°. Spray a 9×13-inch baking dish with nonstick cooking spray.
Combine the brown rice, wild rice, thyme, pepper, onion, celery and mushrooms in the pan. Stir in the broth.
Remove the chicken pieces from the marinade and place them atop the rice mixture.
Cover the pan with foil and bake for 1 hour.
Uncover and bake an additional 30 minutes or until the rice absorbs the liquid and chicken is cooked through and juices run clear. If using chicken breasts, cut each one in half prior to serving.
Serve the chicken alongside the rice.
To prepare this as a freezer meal: Combine chicken breasts and vinaigrette in bag. Label. Combine rice and spices in a second bag. Label. Lay out onion, celery and mushrooms in a single layer on a baking sheet. Flash freeze. Place vegetables in a third bag and make sure to label them. Place all bags together in a larger bag, labelled Chicken and Wild Rice Bake. Be sure to include baking instructions. Freeze. Thaw chicken before baking. Bake as directed above.Promptly store leftovers in an airtight container in the refrigerator, for up to 4 days.Nutritional values are approximate and based on 1 piece of chicken and 1/8 of the rice mixture.