Prepare grill or grill pan to cook chicken over direct medium-high heat.
While the grill is getting set, brush the chicken with olive oil on both sides and season with salt and pepper.
Grill the chicken for about 5 minutes per side, or until juices run clear and the internal temperature is 165 degrees. Remove from grill, and allow to cool.
Meanwhile, boil a large pot of water and prepare pasta according to package directions. Drain well.
Toss the pasta together with pesto, tomatoes, basil and Parmesan cheese.
Slice the chicken into thin strips and place on top of the pasta with additional parmesan cheese and basil, if desired.
This pasta can be served warm or cooled and is delicious either way.