On a grill (preferred), grill pan or skillet, cook chicken breasts until done. Set aside to cool; slice in thin strips.
In a large pasta pot, boil water, salting generously. When water boils, add pasta, setting a timer for the pasta cooking time (according to box instructions).
During the last two minutes of the cooking time, add the asparagus and frozen peas. When pasta is al dente and peas/asparagus are tender, drain into a strainer. Add to a large bowl and toss with pesto and chicken.
If desired, top with freshly shaved parmesan cheese.