Bring water to a boil in a medium-large sauce pot. Add salt and pasta. Cook until al dente, drain, cover and set aside.
Heat grill to high heat, add chicken breasts. Grill until cooked, about 8-10 minutes. Remove and cover with foil.Once cooled, cut into bite size pieces.
Soak asparagus in salt water, to remove any dirt. Dry asparagus on a paper towel to avoid it splatter when adding to the hot skillet. Cut into 1 inch bite size pieces.
Heat a skillet, add olive oil, and asparagus. Sauté for about 5 minutes, long enough that they should still have a crunch. Add the pesto, chicken and pasta and mix well.
Serve immediately and garnish with Parmesan cheese and fresh basil.
