Combine flour, rosemary, and pepper in a shallow dish. Dredge chicken in flour mixture.
Heat 2 teaspoons oil in a large skillet over medium heat.
Add chicken to pan; cook 3 to 4 minutes on each side or until lightly browned.
Remove chicken from pan; set aside.
Heat remaining 1 teaspoon oil in pan over medium heat; saut carrots, onion, and garlic in hot oil 2 minutes.
Add water and broth; bring to a boil. Stir in rice and remainder of seasoning packet; top with chicken. Cover, reduce heat, and simmer 10 minutes or until chicken is done.
Remove from heat, and place chicken on serving plates.
Add spinach to rice mixture, and stir until spinach wilts.