Preheat oven to 425°. Rub chicken pieces with 1 Tbsp. olive oil; sprinkle with 2 tsp. salt and 1 tsp. pepper.
Spread ready-to-serve rice in an even layer in a heavy-duty aluminum foil-lined sheet pan, breaking up clumps.
Cut broccoli into florets. Toss together broccoli florets, 2 Tbsp. oil, 1/2 tsp. salt, and 1/2 tsp. pepper in a medium bowl; spread in an even layer over rice. Toss together mushrooms and remaining olive oil, salt, and pepper, and spread over broccoli and rice.
Place chicken pieces, skin side up, 1 1/2 inches apart on broccoli and mushrooms.
Bake at 425° for about 1 hour or until a meat thermometer inserted in thickest portion of chicken registers 170°. Let stand 5 minutes before serving.