Heat 1 tablespoon of the salad dressing in a large skillet with a tight-fitting lid over medium-high heat.
Add chicken and cook until browned on all sides; remove from skillet and set aside. To the same skillet, heat remaining dressing.
Add mushrooms; cook, stirring frequently, until they begin to release their liquid, about 4 minutes.
Add tomatoes, carrot and reserved chicken. Reduce skillet heat, cover and simmer for 10 minutes or until juices from the chicken run clear when pierced with a fork.
Remove chicken and vegetables to a heated platter. Raise skillet heat to high and cook the sauce until slightly thickened, about 2 minutes. Pour sauce over chicken and sprinkle with green onions.