DO-AHEAD TIP: Prepare bacon.
Heat the oil in a large skillet with a tight-fitting lid over medium-high heat.
Add mushrooms and onion; cook for 5 minutes, stirring occasionally. Stir in tomatoes, salad dressing, and tomato paste.
Add chicken; bring to a boil then reduce heat, cover and simmer for 12 minutes or until chicken is cooked through.
Sprinkle with shredded cheese and crumbled bacon; simmer, uncovered, for 5 minutes or until cheese has melted.