Preheat oven to 350°.
Heat oil in a large ovenproof Dutch oven over medium-high heat. Sprinkle 1/8 teaspoon salt and 1/4 teaspoon pepper evenly over chicken. Add chicken to pan; cook 5 minutes on each side or until browned. Remove from pan; set aside. Add onion and mushrooms to pan, and sauté 5 minutes or until liquid evaporates. Add flour, and cook 1 minute, stirring constantly. Gradually stir in remaining 1/8 teaspoon salt, remaining 1/4 teaspoon pepper, broth, wine, and rosemary. Bring to a boil, scraping pan to loosen browned bits. Return chicken to pan.
Cover and bake at 350° for 30 minutes or until chicken is done. Remove chicken from pan; keep warm. Place pan over medium-high heat; cook 7 minutes or until mushroom sauce is slightly thick, stirring occasionally.