Preheat oven to 450°.
To prepare vegetables, combine squash and next 5 ingredients (squash through oil) in a roasting pan; toss gently to coat. Bake at 450° for 20 minutes.
To prepare chicken, sprinkle chicken with dried basil and oregano.
Place chicken on a grill rack coated with cooking spray; cook chicken 4 minutes on each side or until chicken is done. Cool; cut into 1/4-inch-wide strips.
To prepare vinaigrette, combine vinegar and next 6 ingredients (vinegar through garlic); stir with a whisk.
Combine the roasted vegetables, chicken, vinaigrette, pasta, fresh basil, and tomatoes in a large bowl; toss gently to coat.