Heat oil in a skillet over medium heat.

Sauté chicken in oil until golden, about 5 minutes; drain.

Add broth, wine or broth, garlic, salt, and pepper; bring to a boil.

Reduce heat; cover and simmer for 20 minutes.

Add tomatoes, peppers, and mushrooms.

Simmer, covered, for 15 minutes, or until chicken is cooked through.

Transfer chicken to a serving dish and keep warm.

In a small bowl, combine cornstarch, water, and rosemary; stir into vegetable mixture.

Cook and stir until thickened and bubbly.

Serve chicken over noodles or rice; spoon sauce over chicken.