Make the pasta according to package directions (al dente is about 1 minutes less in cooking time). Allow to cool.
Set a tiny amount of basil, parsley and parmesan aside for final garnish.
Make the dressing: In a small bowl, mix together the vinegar, pesto, garlic, sugar, salt, and pepper. Gradually pour in the olive oil, whisking constantly until combined. Set aside.
Assemble pasta salad: Add the cooked, cooled pasta to a large bowl. Add the tomatoes, small chicken cubes, mozzarella, olives, bell peppers, onion, parmesan, salt, basil, and parsley. Shake the dressing and pour it over the salad, stirring to combine.
Just before serving, toss again to get any dressing that has gone to the bottom of the bowl.
Sprinkle with chopped basil, parsley, and parmesan that was set aside. SERVE!