Heat oven to 375°F. Spray 12x8-inch (2-quart) glass baking dish with nonstick cooking spray.
In sprayed baking dish, combine rice, zucchini, broth, tomatoes and mushrooms; stir gently to mix. Arrange drumsticks over rice mixture. Sprinkle chicken with paprika. Cover with foil.
Bake at 375°F. for 30 minutes. Uncover; bake an additional 10 to 15 minutes or until chicken is fork-tender and juices run clear.