Pat chicken dry with paper towels.
Inject melted into the chicken breasts also coating the outside.
Coat the chicken with Italian Rub.
Cook chicken on the grill with the lid closed for about 25 minutes.
Check internal temperature using a digital meat thermometer, cooking until it reaches 165°.
Remove chicken from the grill and allow to rest about 5 minutes before dicing.
Cook carrots, onions and garlic in olive oil over medium heat, stirring occasionally until vegetables are softened.
Stir in the tomato sauce, diced tomatoes and chicken broth, bringing to a boil.
Stir in the pasta, cooking, stirring often about 5 minutes.
Add the pesto and the diced chicken.
Continue cooking until pasta is tender.
Remove from heat and stir in grated parmesan cheese.
Serve immediately, garnishing with fresh basil and additional parmesan cheese if desired.