Cook and drain pasta according to package directions. While pasta is cooking, season chicken with salt and pepper and place on a grill (or grill pan) over medium-high heat for 6 minutes on each side, until center is no longer pink. You can add other spices if you want, but don’t over-season your chicken, we want the avocado to shine!
Peel avocado and remove pit. Put avocado, basil, salt, pepper, garlic and pine nuts in a blender or food processor. Turn blender on and add olive oil in a slow, steady stream.
Process until mixture becomes a smooth paste. Gently fold in parmesan cheese. Toss with cooked pasta. Slice grilled chicken breasts and lay across top of pasta. Garnish with shaved parmesan cheese and serve.