1. Cook shells in large pot of boiling water.
2. Meanwhile, heat the oil in large, heavy skillet over medium-high heat. Add onion; cook, stirring occasionally, until softened, for about 2 minutes.
3. Add the cubed chicken to the skillet; cook, stirring occasionally, until the chicken loses its raw look, about 2 minutes. Add the coarsely chopped black and green olives, the diced tomatoes and fresh basil. Bring to boiling. Add 1 cup of the pasta cooking water to the skillet, stirring to mix. Return the sauce to boiling over medium-high heat, stirring. Add the salt and pepper to the skillet, stirring to blend.
4. Drain the pasta and toss with the sauce in a large serving bowl until the pasta is well coated. Sprinkle the top with grated Parmesan cheese if desired, or pass the Parmesan cheese, separately, at the table.