In 12-inch nonstick skillet or 4-quart Dutch oven, heat oil over medium-high heat. Add chicken; sprinkle with pepper. Cook 4 to 5 minutes, turning occasionally, until brown.
Stir in frozen vegetables with sauce chips. Reduce heat to medium-low. Cook 10 minutes, stirring frequently, until chicken is no longer pink in center, sauce chips have melted and vegetables are tender.
Stir in basil and Parmesan cheese. Cook 2 to 3 minutes longer, stirring occasionally, until hot.