1. Cook linguine according to package directions, reserving 1 1/2 cups pasta water; drain.
2. Meanwhile, to make the pesto, puree pine nuts, 1 tablespoon oil, garlic and pinch of salt in a food processor until smooth. Add parsley and pulse until just combined, about five times. Add Parmesan and water and pulse five times more. Stir in lemon zest.
3. Pat chicken dry and season with salt and pepper to taste. Heat 1 tablespoon oil in a large skillet over medium-high heat. Add chicken and cook, stirring occasionally, until well browned on all sides, about 5 minutes. Transfer chicken to a plate and set aside.
4. Return skillet to stove and heat remaining oil over medium-high heat. Add onion, season with salt and pepper to taste, and cook until softened, about 3 minutes. Stir in artichoke hearts and cook until slightly broken down, about 3 minutes. Stir in wine, scraping the bottom of skillet. Cook 2 minutes.
5. Add asparagus and cook until crisp-tender, about 2 minutes. Stir in linguine and 1 cup reserved pasta water; add pesto, chicken and peas. Cook until peas are heated through, about 1 minute, adding additional pasta water as needed to loosen sauce. Stir in lemon juice.