Combine oil and garlic in a 9x13 inch baking dish. Add chicken breasts and coat well with the oil and garlic. Sprinkle with the vinegar and Cajun seasoning.
Bake at 350 degrees F (175 degrees C) for 30 minutes.
Remove chicken from oven and cover with green onion and mushrooms; then add a few more sprinkles of oil and vinegar and return dish to oven for 15 to 20 minutes more. Remove from oven and immediately place 1 slice of cheese on top of each chicken breast; cheese will melt. Serve immediately.
