Cook and drain pasta as directed on package. In resealable food-storage plastic bag, place dressing and chicken. Seal bag; refrigerate 15 minutes.
In 12-inch skillet, heat 1 tablespoon vegetable oil over medium-low heat. Cook garlic in oil 1 to 2 minutes or until garlic just starts to brown. Drain chicken, discarding dressing. Add chicken to skillet. Cook chicken 5 to 7 minutes on each side or until juice of chicken is clear when center of thickest part is cut (at least 165°F). Stir in wine; cook until most of the wine has evaporated. Stir in cooking sauce, basil, 1/2 teaspoon salt and 1/4 teaspoon pepper. Heat to boiling; reduce heat. Simmer uncovered 5 to 10 minutes, stirring occasionally, until mixture starts to thicken.
Serve over pasta. Top with Parmesan cheese.