1. Preheat oven to 400°.
2. Combine 2 cups stock, rice, and thyme in a medium saucepan. Bring to a boil. Cover, reduce heat, and simmer 50 minutes. Drain. Stir in 1/2 teaspoon pepper and 1/4 teaspoon salt.
3. Combine remaining 1 cup stock and juice in a small saucepan. Bring to a boil; reduce heat, and cook 20 minutes or until mixture is reduced to 1/3 cup. Remove from heat; stir in arils.
4. Combine turnips, 1/4 teaspoon salt, 1/2 teaspoon pepper, and 1 tablespoon oil in a bowl; toss to coat. Arrange turnip mixture on a baking sheet. Bake at 400° for 20 minutes or until browned and tender, turning once.
5. Sprinkle remaining 1/4 teaspoon salt and 1/4 teaspoon pepper over chicken. Heat a large skillet over medium-high heat. Add remaining 1 tablespoon oil to pan; swirl to coat. Add chicken; cook 4 minutes. Turn chicken, and place pan in oven. Bake at 400° for 8 minutes or until chicken is done.
6. Spoon about 1/2 cup rice onto each of 4 plates. Top evenly with about 1/3 cup turnips and 1 chicken breast half. Drizzle each serving with about 4 teaspoons pomegranate sauce.