Cook pasta as directed on package. Meanwhile, cook chicken and onions in hot oil in large skillet for 6-8 min. or until chicken is done, stirring frequently. Add snow peas, red peppers and garlic; cook and stir 1 min. Remove from heat; cover to keep warm.
Melt butter in medium saucepan. Stir in flour until well blended. Gradually stir in milk. Bring to boil; cook on medium heat 2 min. or until thickened, stirring constantly. Add cream cheese, grated cheese, salt and black pepper; cook 1-2 min. or until cream cheese is completely melted and sauce is well blended, stirring constantly.
Drain pasta; place in large bowl. Add chicken mixture and sauce; toss to coat. Top with parsley.