1. Cook pasta according to package directions, omitting salt and fat; drain well.
2. Combine pasta, chicken, and the next 6 ingredients (through oregano) in a large bowl; toss well.
3. Combine vinegar, oil, salt, and black pepper in a small bowl, stirring with a whisk. Drizzle vinegar mixture over pasta mixture; toss well to coat. Sprinkle with cheese.