Cook pasta as directed on package. Meanwhile, heat oil in large skillet on medium-high heat. Add chicken; cook and stir until no longer pink. Add peppers and mushrooms; cook 3 min., stirring occasionally.
Stir in tomatoes with their liquid and the dressing. Reduce heat to medium-low; simmer 5 min. or until chicken is cooked through.
Toss pasta with chicken mixture. Sprinkle with cheese and basil.